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For Grid leak bias

In electronics, grid leak bias is an early biasing circuit used mainly in antique vacuum tube radio equipment to provide a negative DC bias voltage to the tube's control grid for the purpose of setting its DC operating point. It consisted of a capacitor in series with the grid of the tube, in parallel with a high value resistor called the grid leak, because current "leaking" through the resistor determined the bias voltage. Grid leak bias was used in triode detector stages in early vacuum tube radio receivers which rectified the radio signal; this was called a grid leak detector. It was also used in other vacuum tube circuits that operated with the grid biased near cutoff, such as radio frequency (RF) amplifiers and oscillators.

The grid leak circuit was first used by Lee De Forest the inventor of the triode, in the first primitive triode vacuum tube receivers, but its action was not understood until Edwin Armstrong explained it in 1913. An advantage of the grid leak circuit in early battery-powered radios was that it generated the DC bias voltage from the plate supply by rectifying the grid current that flowed on the positive peaks of the grid waveform, making a separate bias battery unnecessary. Another advantage was that it was somewhat self-adjusting; the larger the AC drive signal on the grid the more negative the bias. Without a signal the grid was biased at zero volts; this allowed vacuum tube oscillators to be self-starting. Grid leak bias was most widely used in early directly-heated triode vacuum tubes. It became largely obsolete after indirectly-heated tubes were developed in the later 1920s, in which the necessary grid bias voltage could be generated by the cathode circuit using cathode bias. Today it is only found in some high power vacuum tube radio transmitter circuits and industrial RF heating equipment, and in antique tube-type radio receivers.

How it works

A grid leak bias circuit consists of a capacitor and resistor in the grid circuit. The bias voltage is developed by rectifying the grid current that flows when the grid is positive with respect to the cathode. The simplest form is the shunt grid leak circuit C_g R_g, right. Before a signal is applied to the grid, it has a DC voltage of 0V. When an alternating current (AC) input signal voltage is applied, during the positive half-cycles the grid has a positive voltage with respect to the cathode and thus a positive charge. This attracts some of the negative electrons which are emitted from the cathode, and they strike the grid, causing a current of electrons into C_g, which charges the capacitor plate attached to the grid with a negative charge. During the negative half-cycles of the input signal, the grid is negative with respect to the cathode so no grid current flows. Thus over the first few cycles, a negative voltage builds up on the capacitor, biasing the grid with a negative charge. As more

If there was no resistor, the voltage would build up on C_g until it reached the tube's cutoff voltage and no electrons would reach the plate, the plate current would be cut off. The grid leak resistor R_g provides a path for charge to "leak" slowly off the capacitor. The path of the electrons is from C_g's negative plate, through R_g, the signal source, and to the capacitor's positive plate. However, since R_g has a large value, not all of the charge deposited on the capacitor during the positive half-cycle leaks off, so the voltage on C_g increases. As the average voltage on the capacitor increases, it biases the grid more negative, so the grid is positive for a smaller proportion of each cycle, reducing the current into the capacitor; at the same time the increased voltage causes the current through R_g discharging it to increase. After a few cycles an equilibrium voltage is reached, where the average current from the grid each cycle is equal to the average current through R_g. The voltage drop across R_g is the grid bias voltage.

Another way to look at the grid leak bias circuit is as a rectifier circuit. The cathode-grid diode rectifies the input AC drive voltage to DC, C_g serves as a filter capacitor to smooth the DC, and R_g serves as the load. The bias voltage is equal to the output of the voltage divider made by R_g and r_cg the cathode to grid resistance of the tube.

Grid-leak detectors

A major use of grid-leak bias during the vacuum tube era was in the grid leak detector, used as a detector (demodulator) circuit in vacuum tube receivers. It's function was to extract the modulation (audio signal) from the radio frequency carrier wave by rectifying the carrier, allowing only It consisted of a grid leak biased triode biased near cutoff. An advantage of the grid leak detector over was that acted as an amplifier as well as a detector.

For Grid leak

In electronics a grid leak was a simple biasing circuit used in older vacuum tube electronic equipment to provide a negative DC voltage on the grid of the tube. It was used in detector stages in vacuum tube radio receivers which served to rectify the radio signal, this was called a grid leak detector. It was also used in vacuum tube oscillator circuits, where it had the advantage of making the oscillator self-starting. It consists of a capacitor connected in series with the tube's control grid electrode, in parallel with a high value resistor through which excess charge "leaks" off to ground. The grid leak circuit was invented by Lee De Forest in his early Audion (triode) vacuum tube radio receivers but its action was a mystery until Edwin Armstrong explained it in 1913. The advantage of the grid leak circuit was that it generated the necessary negative DC bias voltage from the rectifying action of the tube itself, eliminating the need for a separate negative power supply or battery. The development of indirectly heated cathode tubes in the mid 1920s made grid leak bias mostly obsolete since negative grid bias voltage could be generated from the plate supply, using the cathode bias circuit.

Grid current

In a triode vacuum tube, electrons given off by the heated filament, (the cathode), are attracted to the anode (plate electrode) which has a positive voltage. The voltage on the grid, located between cathode and anode, controls the anode current. As the grid voltage becomes more negative, it allows fewer electrons through to the anode, and anode current decreases. When the grid voltage becomes negative enough (usually a few volts), the anode current is reduced to zero, this is called the tube's cutoff voltage.

In a radio receiver envelope detector the tube must conduct anode current only on the positive half cycles of the radio frequency carrier wave, thus rectifying the wave. This is accomplished by adding to the AC signal voltage applied to the grid a steady negative DC voltage - a bias - equal to the cutoff voltage. Thus on the negative half cycles of the signal the voltage on the grid will be below its cutoff voltage, and no anode current will flow.

As long as the voltage on the grid is negative, below the cathode voltage, no electrons will be attracted to the grid itself, and no current will flow in the grid circuit. However if the voltage on the grid becomes positive with respect to the cathode voltage, some electrons will be attracted to it and flow out of it into the grid circuit. In this case the grid-cathode electrode pair acts like a diode, passing current in one direction. In the grid leak bias circuit that DC current is used to charge a capacitor to provide the negative DC bias voltage.

How grid leak bias works

In the grid leak circuit a capacitor is inserted in series between the grid and the signal source. On each positive half-cycle of the signal voltage the grid will become positive and electrons will flow out of the grid and charge the right capacitor plate negative. The voltage applied to the grid is the sum of the AC signal voltage and the DC voltage on the capacitor, so the capacitor provides a negative bias. However as long as the negative voltage on the capacitor is less than the positive peak signal voltage, the grid will be positive for a portion of the cycle, and grid current will continue to charge the capacitor more negative. Without the resistor, the capacitor will keep accumulating negative charge until (within a few cycles) it reaches the cutoff voltage of the tube, and the anode current stops flowing.

To prevent this, a high value resistor, the "grid leak", is connected between the capacitor and ground (the cathode). The current through this resistor bleeds off some of the negative charge on the capacitor. The time constant $\scriptstyle R_{g}C_{g}$ of the RC filter is made much longer than the signal period, so the voltage on the capacitor is substantially constant and does not decline appreciably between the pulses of grid current. As the bias on the grid becomes more negative, fewer electrons are attracted to the grid and the grid current decreases. At the same time the increasing capacitor voltage causes more current to flow through the resistor. Within a few cycles it reaches an equilibrium at which all the charge accumulated on the capacitor plate each cycle bleeds off through the resistor (another way of saying this is that the average grid current equals the average resistor current). The capacitor stops charging and the DC bias voltage on the grid is constant.

Types

There were two ways of connecting the grid leak circuit:

• If the signal source provided a DC path to ground (the cathode), such as a parallel tuned circuit or transformer, the grid leak resistor could be connected in parallel with the capacitor. The grid current would flow from the grid through the resistor, through the signal source, and back to the cathode.
• If the signal source did not have a DC path to ground, the resistor would be connected between the grid and ground (cathode). The grid current would flow through the resistor directly to the cathode.

For Dipole antenna

Animation of a half-wave dipole antenna transmitting radio waves, showing the electric field lines. The antenna in the center is two vertical metal rods, with an alternating current applied at its center from a radio transmitter (not shown). The voltage charges the two sides of the antenna alternately positive (+) and negative (−). Loops of electric field (black lines) leave the antenna and travel away at the speed of light; these are the radio waves.

Animated diagram of a half-wave dipole antenna receiving energy from a radio wave. The antenna consists of two metal rods connected to a receiver R. The electric field (E, green arrows) of the incoming wave pushes the electrons in the rods back and forth, charging the ends alternately positive (+) and negative (−). Since the length of the antenna is one half the wavelength of the wave, the oscillating field induces standing waves of voltage (V, represented by red band) and current in the rods. The oscillating currents (black arrows) flow down the transmission line and through the receiver (represented by the resistance R).

How it works

A dipole antenna is a resonant linear antenna; a pair of metal rods that acts as a dipole source of radio waves but also as a linear stub resonator. When driven by an electric current from a transmitter near one of its resonant frequencies, in addition to radiating radio waves, the rod stores oscillating electrical energy in the form of electric current reflecting back and forth between its ends, with the currents interfering to form standing waves. The advantage of this is that the standing wave current in the antenna is much larger than the feed current from the transmitter. The power radiated as radio waves is proportional to the square of the antenna current, so an antenna driven at a resonant frequency radiates far more power than the same antenna driven by the same magnitude of current at a nonresonant frequency.

The ratio of the standing wave current to input current is a parameter called the antenna's Q_factor, so an antenna radiates $Q^{2}$ more power for a given input current at resonance than off resonance. The $Q$ of a typical dipole antenna can be 10-15, so it radiates 100-200 times as much (10-13 dB more) power at resonance than when nonresonant.

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If radio waves strike a straight metal rod, the oscillating electric field of the waves will exert a force on the electrons in the rod, causing them to move back and forth along the rod, creating an oscillating electric current along the rod. The current is proportional to the component of the electric field parallel to the rod axis; so as an antenna it responds best to linearly polarized radio waves. During the half cycle when the electric field is directed toward one end of the antenna rod, the current will cause a positive charge to accumulate at that end and a negative charge to accumulate at the other end. During the next half cycle, when the electric field of the wave reverses it causes a current in the other direction, causing the charges on the ends of the rod to reverse.

The amount of power the rod absorbs from the radio waves is greater at some frequencies than at others because due to its inherent capacitance and inductance the rod acts as a resonator for electric current. The oscillating current induced by the radio waves reflects back and forth between the ends of the rod. If the frequency of the radio wave is such that an electrical signal makes a round trip from one end of the rod to the other and back in an integral number of periods of the oscillation, the reflected waves will reinforce (constructively interfere) the induced waves, creating sinusoidal standing waves of current and voltage in the rod. These frequencies are called the resonant frequencies of the antenna. Since the current must go to zero at the ends of the rod, the ends must be nodes of the current standing wave. The nodes of a sine wave occur every half wavelength $\lambda /2$, so the condition for resonance is that the electrical length of the rod must be an integral number of half-wavelengths. The shortest rod which satisfies this condition is a half-wavelength long. Half-wavelength dipole antennas are most widely used. In a half wave dipole, the oscillating current standing wave increases from zero at the ends to a maximum in the center of the rod, while the voltage standing wave is maximum at the ends and decreases to zero (a node) at the center.

In a rod not connected to anything else, the radio wave power absorbed by the rod is just reradiated (scattered). To deliver the radio power to an electrical load, such as a radio receiver, the rod is divided into two parts and a load is connected between them, so the current flowing back and forth between the two halves passes through the load. This is a dipole receiving antenna.

The antenna can also be connected to a transmitter which applies an oscillating current to the two halves of the rod, charging them alternately positive and negative. The alternating charges on the two ends create an oscillating electric field along the rod, while the oscillating current in the rod creates an oscillating magnetic field circling the rod. If the frequency of the current is in the radio frequency range, the coupled fields will radiate away from the rod as electromagnetic waves, radio waves.

For Magnetism

Elementary principles

Magnetism is the theory of how magnetic fields interact with matter. A magnetic field is one of the fundamental physical forces between matter; with the electric field it constitutes the electromagnetic interaction, one of the four fundamental forces of nature. Physics distinguishes several different types of magnetism; mechanisms by which a magnetic field acts on matter, which occur in different substances. Diamagnetism, paramagnetism and antiferromagnetism cause weak forces, which can only be detected in a laboratory. Ferromagnetism (including ferrimagnetism), in contrast, creates the strongest forces; it is this mechanism that is responsible for creating magnets and all the magnetic effects seen in everyday life. This section will explain the simpler principles of ferromagnetism, mostly without mathematics, using an approximation called the magnetic pole model of a magnet.

Magnets

A bar magnet, a permanent magnet in the shape of a straight bar

Main article: Magnet

A device or material that generates a magnetic field is called a magnet. There are two types of magnet, permanent magnets and electromagnets, described below. Most magnets have two locations where the magnetic field seems to emerge from the magnet, called magnetic poles. Every magnet has a north (N) pole and a south (S) pole. It is not possible to separate the poles to have an isolated north pole or south pole. If a permanent magnet is cut in two between its poles, the end with the north pole will have a new south pole at the cut surface, while the end with the south pole will have a new north pole, resulting in two dipolar magnets. This cutting process could be continued until the magnet is divided into molecules, and still no individual north or south pole would be found, because the sources of the field in a permanent magnet are atomic particles (electrons) which are themselves magnetic dipoles.

Magnetic field lines

Main article: Field line

Drawing magnetic field lines

Drawing of magnetic compasses near a bar magnet.

Bar magnet on a compass board. The magnetized compass needles turn parallel to the magnetic field

Drawing lines parallel to the direction of the compass needles, a field line diagram can be created

Magnetic field of an ideal bar magnet calculated by computer

The field lines enter a magnet at the south pole (left), pass through it and exit at the north pole (right)

More complicated magnetic field surrounding two magnets at right angles

Magnetic fields are invisible, but their shape can be shown with a diagram called a field line diagram. A magnetic field is a vector field, which means it has a magnitude (strength) and direction at each point in space. So one way to diagram a magnetic field is to draw little arrows at intervals throughout the space. The direction of the field at each point is the direction that a small bar magnet free to turn in three dimensions, like a compass needle, would point in the field (see pictures). By convention, the direction the north end of the bar magnet points is defined as the direction of the field. The field strength is proportional to the force that would be exerted on a magnet's north pole at that point.

Alternatively, the direction of a magnetic field can be displayed by a visual aid called a field line. This is a line that is tangent (parallel) to the direction of the field at each point along its length, which has an arrowhead which points in the direction of the magnetic field vector: away from the north pole of the magnet and toward the south pole. A field line can be drawn by starting at a point and moving through space continuously in the direction that a compass needle points, following the field direction. By drawing a collection of neighboring field lines filling space the shape of the field can be displayed; this is a field line diagram. Since a three-dimensional diagram of lines is visually confusing, field line diagrams are often two-dimensional, showing the field in a flat plane section of space.

Since a magnetic field has a unique direction at each point at which it is nonzero, field lines can never intersect. A magnetic field is divergenceless (solenoidal), which means that magnetic field lines don't have endpoints; they either extend to infinity in both directions or are closed loops. A magnet creates a type of field called a dipole field; the magnetic field lines are closed loops that pass in parallel in the same direction through the magnet. The field lines emerge at the magnet's north pole, circle around through space to the south pole of the magnet, and enter through the south pole. The strength of the field at a point is indicated by the number of field lines passing though a unit area. As the field lines approach a magnetic pole they converge closer together, indicating the field is stronger there. The unit of magnetic field strength is the tesla (T).

The looping geometry of magnetic field lines explains why an isolated magnetic pole cannot exist. A north magnetic pole is just the area on a magnet at which most of the field lines exit it. The south pole is the area where most field lines enter it. Every field line which enters a magnet must exit it again, so magnetic poles must come in north-south pairs of equal strength. There are some magnetic fields which are not dipolar, they do not have poles; for example the field lines of the magnetic field around a straight current-carrying wire are in the form of concentric circles, and do not emerge from magnetic poles. Some specially-shaped magnets have greater numbers of pole pairs: quadrupole magnets have two north poles and two south poles, sextapole magnets have three, and octopole magnets have four.

Forces between magnets

The fields of two bar magnets attracting each other

The fields of two bar magnets repelling each other

The forces and torques between magnets are determined by the forces between their poles.

Magnets exert force on each other. The force is concentrated at two points on a magnet, at its poles

• Unlike poles attract; north poles and south poles attract each other
• Like poles repel; two north poles or south poles will repel each other

This is analogous to the force rules between electric charges: unlike charges attract while like charges repel. The force between two poles is proportional to the product of the strength of the magnetic fields and inversely proportional to the square of the distance between them. Since each (dipole) magnet has a north and a south pole of equal strength, and the force decreases with distance, the net force between two magnets is dominated by the force between the poles which are nearest to each other. If the two magnets' nearest poles have opposite polarity, the magnets will attract, while if they have the same polarity they will repel. Because the net force on the magnet is equal to the difference between the attractive force of the unlike pole and the repulsive force of the like pole, when two magnets are far apart the force between them decreases approximately with the inverse cube of the distance between them.

A uniform (homogeneous) magnetic field, which has a constant strength and direction, exerts no net force on a magnet, because the force on the north pole is equal and opposite to the force on the south pole. However, it exerts a torque (below).

The polar model of a magnet used here, which assumes that all the force on a magnet is concentrated at its poles, is an approximation which becomes inaccurate when the magnets get too close. If the pole of one magnet gets too near the side of another, it will alter the magnetic field lines inside; some of the magnetic field lines will not exit through the poles but will pass through the side of the magnet, so the force will depend in a complex way on the shape of the magnets. The precise force and torque between magnets is determined by the shape of their magnetic field, which can be calculated by computer.

Torque on a magnet

Since the force on a magnet is exerted at two locations, the poles, magnets also exert torque on one another. If a bar magnet is mounted on a pivot so it can turn, approaching it with the pole of a second magnet will cause the unlike pole to be attracted while the like pole will be repelled, exerting a torque on the pivoted magnet that will cause it to turn until the axis of the magnet is parallel to the magnetic field, with the unlike pole nearest to the external pole and the like pole furthest away. The torque exerted by a magnetic field on the pivoted magnet is equal to the product of the strength of the external field, the strength of the magnet, the length of the magnet, and the sine of the angle between the magnet's axis and the field.

Definition of north and south poles

The Earth's magnetic field is similar to that of a bar magnet

A cheap magnetic compass. The end of the needle painted red is always the north pole

Main article: Earth's magnetic field

The origin of the names of the poles is geographical, because the Earth itself acts like an enormous magnet and has a magnetic field, the geomagnetic field, created by electric currents deep inside. So a bar magnet mounted on a low-friction pivot will align in parallel with the horizontal component of the Earth's field; this is the principle of the magnetic compass. The north (or "north-seeking") pole of a magnet is defined as the one attracted to the Earth's Northern magnetic pole located in the Arctic near Greenland, while the south ("south-seeking") pole of a magnet is attracted to the Earth's Southern magnetic pole located near Antarctica. Since opposite poles attract, the Earth's Northern magnetic pole is actually the south pole of the Earth's field, while the Earth's Southern magnetic pole is actually the north pole of the field. The Earth's magnetic poles are located close to its geographic North and South poles, although not exactly at them, so a compass needle will point in a north-south direction, and the first use for magnets was in compasses for navigation.

Permanent magnets

Main articles: Magnet and Ferromagnetism

A "horseshoe magnet" made of alnico. The two poles, at the bottom ends, are bridged by a keeper

Ferrite magnets. The poles are on the wide faces

Neodymium magnets

A magnetic field can be generated in only two ways: by an electric current (moving electric charges), or by particles called magnetic dipoles in materials. An electron, in addition to its electric charge, is a magnetic dipole; it acts like a tiny bar magnet, creating a dipole magnetic field around it due to its spin. One end of the electron is a north pole while the other end is a south pole. A piece of material which generates a persistent magnetic field due to internal magnetic dipoles is called a permanent magnet. Only substances which are ferromagnetic (or ferrimagnetic) can become permanent magnets; these are also the materials that are strongly attracted to a magnet. Ferromagnetism is an unusual property which occurs in only a few materials; the common ones are iron, nickel, cobalt, and their alloys, and some compounds of rare earth metals like neodymium and samarium.

The unique property of ferromagnetic substances is that their electron dipoles spontaneously align in the same direction, with the north poles all pointed in one direction and the south poles in the other. When this happens the weak magnetic fields of the electrons combine (superpose) into a strong magnetic field which extends out of the material into the space around it, making the material a magnet. The side of the material toward which the north end of the dipoles are directed becomes its north magnetic pole, while the side toward which the south ends are directed becomes its south magnetic pole.

Magnetized and unmagnetized materials

The above would seem to imply that every piece of ferromagnetic material should have a magnetic field, since the electron fields are aligned, but ferromagnetic substances like iron are often found in an unmagnetized state. This is because a piece of ferromagnetic material is divided into microscopic regions called magnetic domains. Within each domain the electron dipoles are aligned parallel, creating a field. In a piece of ferromagnetic material in its natural state the dipoles in different domains tend to point in random directions, so their weak magnetic fields cancel out and the piece of material has no net magnetic field, it is said to be unmagnetized. However if it is subjected to a strong external magnetic field, it can become magnetized; the magnetic field passes through the material and aligns the electron dipoles of the separate domains to point in the same direction so it generates a magnetic field, which persists after the external field is removed; this is called a "permanent magnet".

In spite of the name, permanent magnets can be demagnetized. If the magnet is heated, or subjected to vibration by hammering, or an alternating magnetic field is applied by a degaussing coil, the agitation of the molecules will cause the dipoles to lose alignment and point in random directions again, so the piece of material will lose its magnetic field and return to an unmagnetized state. Commercial magnets are manufactured using metallurgical processes that align the microcrystalline structure of the ferromagnetic material in a strong magnetic field during manufacture, so the parallel orientation of the dipoles is built into the material, making them very difficult to demagnetize.

Force between a magnet and ferromagnetic material

A magnet exerts an attractive force on nearby pieces of unmagnetized ferromagnetic material like iron. Both the north and south poles of a magnet attract iron, with equal force. This occurs because the magnetic field temporarily magnetizes the iron; this is called induced magnetization. If the north pole of a magnet is brought near a piece of iron, the field lines will pass through the iron and align the electron dipoles, inducing a south magnetic pole in the side of the iron nearest to the magnet, and a north pole on the side away from the magnet. Since the induced south pole is nearest to the north pole of the magnet its attraction is greater than the repulsion of the induced north pole, resulting in a net attractive force. If the magnet's south pole is brought near, the polarity of the induced poles will be reversed, again causing attraction.

As with magnets, ferromagnetic material is only attracted by an inhomogeneous (nonuniform) magnetic field; a piece of iron is attracted to a magnet because the magnetic field is higher near the magnet. A uniform field exerts no net force because it exerts equal and opposite forces on the induced N and S poles, but it does exert a torque on the metal. When the magnet is removed, most of the induced magnetism of the iron disappears, although some remanent magnetism may remain.

Magnetic field of an electric current

Main article: Ampere's circuital law

An electric current, a moving stream of charged particles such as electrons in a wire, creates a circular magnetic field around it due to Ampere's circuital law. The magnetic field lines around a straight current-carrying wire form concentric circles in a plane perpendicular to the wire. The field strength is proportional to the current, and inversely proportional to the distance from the wire. The direction of the magnetic field can be determined by the right hand rule; if the right hand is wrapped around the wire with the thumb pointing in the direction of the current (conventional current, flow of positive charge) the fingers will be pointing in the direction the magnetic field lines circle the wire.

Electromagnets

Magnetic field of loop of wire

Electromagnet, consisting of wire wound around an iron core

Main article: Electromagnet

A current-carrying loop of wire generates a dipole magnetic field; the field lines are loops that pass in parallel through the wire loop, similar to the way field lines pass through a bar magnet. One side of the wire loop is a north pole, the other a south pole.

A stronger field can be generated by winding multiple turns of wire into a coil or helix, so the magnetic fields of the individual loops reinforce. When a current is passed through the wire, it will create a dipole magnetic field similar to a bar magnet; the magnetic field lines pass through the center of the coil, making one end of the coil a north pole and the other end a south pole. This is called an electromagnet. The strength of the magnetic field increases with the current; when the current stops the magnetic field disappears. The direction of the magnetic field can be determined from the current by the right hand rule. If the right hand is wrapped around the coil with the fingers pointing in the direction of the current (conventional current, flow of positive charge), the thumb will be pointing to the end of the electromagnet that is the north pole.

An electromagnet can be made much stronger by winding the wire around a piece of ferromagnetic material like iron. This is called a ferromagnetic-core or iron-core electromagnet. When the current through the wire is turned on, the wire's magnetic field temporarily magnetizes the iron, turning it into a magnet, and the field of the iron adds to the wire's magnetic field, strengthening it. A ferromagnetic core can increase the magnetic field strength of an electromagnet by a factor of hundreds of times. After the current is turned off, the iron's electron dipoles lose alignment so its magnetic field largely disappears, although some magnetization may remain, leaving the iron a weak magnet; this is called remanent magnetism.

Force of a magnetic field on a moving charge

The Lorentz force of a magnetic field bends a beam of moving electrons into a circle.

Main article: Lorentz force

A magnet exerts no force on a stationary electric charge, but it exerts a force on a moving charge. This is called the Lorentz force. The force is perpendicular to both the magnetic field and the direction the particle is moving. Its magnitude is equal to the product of the magnitude of the charge, the strength of the magnetic field, the velocity of the particle, the sine of the angle between them. Therefore there is no force on a particle moving in the direction of the magnetic field. The direction of the force can be determined from the direction of the motion and the field direction by the right hand rule.

Due to the Lorentz force a wire carrying a current that is moving through a magnetic field in a direction so the wire crosses the field lines, has a force on it perpendicular to the wire and the field lines. The force is equal to the product of the current, the magnetic field strength, the velocity of the wire, and the sine of the angle between them. This Lorentz force on a current carrying wire is the force that turns an electric motor.

Electromagnetic induction

Main article: Electromagnetic induction

A changing (time varying) magnetic field creates a circular electric field (an electromotive force or EMF) perpendicular to the field due to Faraday's law of induction. When the changing magnetic field passes through a closed loop of wire, the EMF exerts a force on the mobile electrons in the wire, generating an electric current. The strength of the EMF is proportional to the strength of the magnetic field, the rate of change of the field, and the area of the loop. This effect, called electromagnetic induction, is the operating principle behind electric generators and transformers.

The current in the wire will in turn create its own magnetic field, called a counterfield. The direction of the current induced in the wire can be determined by Lenz's law; which states it will create a counter magnetic field which opposes the change in magnetic field through the loop. For example, a horizontal wire loop with a magnetic field passing through it in a downward direction which is increasing will induce a counterclockwise current in the wire, which will generate a counterfield directed up, opposite to the direction of the applied field, tending to oppose the increase in magnetic field. A downward magnetic field which is decreasing, in contrast, will induce a current in a clockwise direction, which will generate a counterfield directed down, in the same direction as the applied field, tending to maintain the magnetic field and oppose its decrease.

References

• Halliday, David; Resnick, Robert; Walker, Jearl (2013). Fundamentals of Physics, 10th Ed. John Wiley and Sons. ISBN 9781118230718.
• Serway, Raymond; Faughn, Jerry; Vuille, Chris (2008). College Physics, 8th Ed. Vol. 10. Cengage Learning. pp. 626–628. ISBN 9780495386933.
• Giordano, Nicholas (2009). College Physics: Reasoning and Relationships. Cengage Learning. pp. 649–650. ISBN 9780534424718.

For Electric field

Description

Electric charges exert forces on one another across a distance; like charges attract while unlike charges repel. Coulomb's law states the force between two point charges is equal to the product of the charges divided by the square of the distance between them. Since a charged object will exert forces on other nearby charged objects at a distance without any visible connection, the concept of a field was invented, which surrounded the charged object and which exerted the force. An electric field is a mathematical function (vector field) $\mathbf {E} (\mathbf {x} )$ giving the magnitude and direction of the force that would be exerted on a unit electric charge at each point of space $\mathbf {x}$ due to a collection of source charges. Since the force due to multiple charges is equal to the vector sum of the forces of each charge, the net electric field at a point is similarly equal to the sum of the field of each individual charge acting separately. Once the electric field has been determined, it allows the force $\mathbf {F}$ on any charge $q$ to be calculated easily, by multiplying the electric field $\mathbf {E} (\mathbf {x} )$ at the charge's location by the magnitude of the charge: $\mathbf {F} =q\mathbf {E}$. An electric field has units of newtons per coulomb or equivalently volts per meter. The shape of the electric field surrounding charges is often displayed with a field line diagram.

Although the definition above gives the impression that an electric field is not "real", but is just a mathematical technique for calculating a charge's force at a distance, the field has other qualities that indicate that it is a "real" property of space. An electric field stores electrostatic energy; work must be done to create it. For that reason it also has inertia and therefore mass, although the mass of everyday electric fields is infinitesimal. Also, a change in the location of a source charge doesn't cause a change in the force on a remote charge immediately, but after a delay proportional to the distance. A movement of an electric charge creates a change in the force exerted on other charges which travels away from the source charge in all directions at a constant speed, the speed of light. This implies that there must be some local property of space, the electric field, which is the medium which transports the change in force and maintains the original force on the remote charge, until the change in force propagates to the remote location. This is called the principle of locality. A changing electric field, coupled with a changing magnetic field in an electromagnetic wave carries energy, momentum and angular momentum through space, and conservation of energy, momentum, and angular momentum do not hold unless these field quantities exist. The oscillating electric and magnetic fields which constitute starlight can be seen, even if the star which is the source of the fields has gone out long ago while the light was traveling to Earth. The uncertainty principle of quantum mechanics causes weak time-varying electric and magnetic fields called vacuum fluctuations (virtual photons) to appear spontaneously throughout empty space, although they can only be detected indirectly. All of these observations indicate that an electric field, although created by electric charges, is a property of space itself.

In physics all forces between matter are caused by fields. The electric field and magnetic field are interrelated and together constitute the electromagnetic field, one of the four fundamental forces of nature. Electric fields are widely used throughout technology, they are the basis of electrical technology and electronics. On a microscopic scale electric fields are the attractive force between electrons and atomic nuclei that hold atoms together, and make up the chemical bonds which are responsible for chemical compounds. Mechanical forces between objects are also electrical in nature; at an atomic scale, when a solid object exerts force on another object it is due to the electric fields of the electrons of the atoms on one object's surface exerting force on the electrons of the atoms on the surface of the other object.

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Electric field lines

Electric fields are created by charged particles or time varying magnetic fields, and exert force on charges. The electric field at a location is defined as the Coulomb force per unit charge exerted on a small positive test charge at the location. An electric field line is a line that is everywhere tangent (parallel) to the electric field. It's direction at any point is the direction of the force on a small positive test charge at that point.

• Electrostatic field lines begin on positive charges and end on negative charges, or extend to infinity. Time varying magnetic fields can create closed loops of electric field due to electromagnetic induction (Faraday's law of induction).
• Electric field lines can only intersect at their endpoints. This is because an electric field has a unique direction at each point at which it is finite and nonzero. At point charges the electric field has an infinite magnitude, so it has no direction, so multiple field lines can emerge from or end on a point charge.
• A field line that begins on a certain quantity of positive charge must end on the same quantity of negative charge. This is due to Gauss's law
• Electrostatic field lines cannot penetrate conductors. This is because conductors contain mobile charges, so an electric field inside a conductor would cause a motion of charge that would create opposing induced charges that would cancel the field. So field lines intersecting conductors must originate from a charge on the surface of the conductor
• Electrostatic field lines intersect conductive surfaces normal (perpendicular) to the surface. This is because a conductive surface cannot have a tangential component of field; the electric field parallel to the surface would cause a flow of current.
• Electric field lines are attracted to dielectric materials and preferentially pass through them. An electric field line passing into a dielectric material will polarize the dielectric, inducing a negative charge on the surface it enters and a positive charge on the surface it leaves, and will have a discontinuous change of direction at the surface.
• Electric field lines exert an attractive force along their length. Two unlike charges linked by electric field lines will be attracted to each other.
• Electric field lines exert a repulsive force on other field lines perpendicular to their length.
• An electric field line diagram can represent the magnitude of the field by letting each field line represent a fixed quantity of flux. Then the field lines are equally spaced in an area of constant field. The closer the field lines are the stronger the field; field lines get closer together as they approach a source. The number of field lines leaving or entering a point charge is proportional to the charge. The electric flux through a given surface is proportional to the number of field lines passing through the surface.

Magnetic field lines

Magnetic field lines are created by electric currents or magnetic dipoles and exert forces on moving charges or magnetic dipoles. The magnitude and direction of the field at any point is given by the force on a moving charged particle from the Lorentz force law. A magnetic field line is a line which is tangent (parallel) to the magnetic field at each point along its length. It's direction at any point is the direction that the north pole of a small magnetic dipole like a compass needle would point.

• Magnetic field lines have no endpoints, they either extend to infinity in both directions, or are closed loops.
• Magnetic field lines can never intersect, since the field has a unique direction at any point.
• Magnetic field lines are attracted to high permeability materials, ferromagnetic or ferrimagnetic materials such as iron or ferrite, and preferentially pass through them. The field lines polarize the material, causing the atomic magnetic dipoles to align in parallel with the field lines.
• A magnet creates a dipole magnetic field consisting of looping field lines that pass in parallel through the magnet. The surface area where the field lines emerge from the magnet is called its north pole. The lines circle around through space to the other side of the magnet and enter through the magnet's south pole.
• A straight current-carrying wire has a magnetic field consisting of concentric circular field lines that circle the wire. The direction of the field lines can be found from the right hand rule; if the wire is grasped with the right hand so the thumb points in the direction of the conventional current in the wire, the fingers will point in the direction the field lines circle the wire.