# Relationship between magnetic field and induced current in a metal loop

Any change in the magnetic environment of a coil of wire will cause a voltage coil, moving the coil into or out of the magnetic field, rotating the coil relative to the Faraday's law is a fundamental relationship which comes from Maxwell's equations. The induced emf in a coil is equal to the negative of the rate of change of. The magnetic poles of the induced current loop are also shown in the Then using Equation for the emf induced in a strait wire in a magnetic field we have. Angle of the wire/current relative to the magnetic field lines. Picture When using a coil of wire the effect of the force is magnified by the number of coils, n, there are: Picture You do not need to know the meaning of this equation for A-level.

Your thumb is going to point straight up. This is the palm of-- that's your thumb. This could be your nail, fingernail, fingernail of your thumb, fingernail of your middle finger. This is the direction of the velocity. Let me get a suitable color.

The velocity is that way. The magnetic field is popping out of the page. So the force on the particle-- on this charged particle or on this charge-- due to the magnetic field is going to go in the direction of your thumb.

So the direction of the force is in this direction. So what's going to happen? There's going to be a net force in this direction on the charge. And the charge is going to move upwards, right? I mean, when you start having a moving-- you could imagine also that you had multiple charges, right?

If you had multiple charges here and you're moving the whole wire, all of those charges are going to be moving upwards. And what is another way to call a bunch of moving charges along a conductor? Well, it's a current, depending on how much charge is moving per second. So at least in very qualitative terms, you see that when you move a wire through a magnetic field or when you move a magnetic field past a wire, right?

Because they're kind of the same thing, it's all about the relative motion. But if you move a wire through a magnetic field, it is actually going to induce a current in the wire.

It's going to induce the current in the wire, and actually this is how electric generators are generated. And I'll do a whole series of videos on how you-- you know, if you're using coal or steam or hydropower, how that turns, essentially that turns these generators around and it induces current. And that's how we get electricity from all of these various energy sources that essentially just make turbines turn.

But anyway, let's go back to what we were doing. So let me ask you a question.

## Faraday's Law

If this particle-- and this all has a point-- if this particle starts at the beginning. Let's say the particle is right here.

So it starts right where the magnetic field starts affecting the wire. And how much work is going to be done on the particle by the magnetic field? Work is equal to force times distance, where the force has to be in the same direction as the distance, right? Force times distance, I won't mess with the vectors right now. But they have to be in the same direction. So how much work is going to be done on this particle? So the work is going to be the net force exerted on the particle times the distance.

Well, this distance is L, right? We say, once a particle gets here there's no magnetic field up here, so the magnetic field will stop acting on it. So the total work done: Work, which is equal to force times distance, is equal to-- so the net force is this up here. Q-- and I'll leave some space-- V cross B times the distance. And the distance right here is just a scalar quantity, so we could put it out front, right?

Q times L times V cross B, right? This is-- Q V cross B is the force times the distance. That's just the work done. Now how much work is being done per charge, right? This is how much work is being done on this charge. But let's say there might have been multiple charges, so we just want to know how much work is done per charge.

So work per charge. We could divide both sides by charge. So work per charge is equal to this per charge.

### Induced current in a wire (video) | Khan Academy

So it is equal to the distance times the velocity that you're pulling the wire to the left with cross the magnetic field. This is where it gets interesting. Briefly stated, Faraday's law says that a changing magnetic field produces an electric field.

If charges are free to move, the electric field will cause an emf and a current. For example, if a loop of wire is placed in a magnetic field so that the field passes through the loop, a change in the magnetic field will induce a current in the loop of wire. A current is also induced if the area of the loop changes, or if the area enclosing magnetic field changes. So it is the change in magnetic flux, defined as that determines the induced current. The last equality removing the integral is valid only if the field is uniform over the entire loop.

Faraday's Law says that the emf induced and therefore the current induced in the loop is proportional to the rate of change in magnetic flux: It is similar in concept to voltage, except that no charge separation is necessary. The magnetic flux FB equals the magnetic field B times the area A of the loop with magnetic field through it if a the magnetic field is perpendicular to the plane of the loop, and b the magnetic field is uniform throughout the loop.

For our purposes, we will assume these two conditions are met; in practical applications, however, magnetic field will vary through a loop, and the field will not always be perpendicular to the loop. Since all applications of Faraday's Law to magnetic storage involve a coil of wire of fixed area, we will also assume that c the area does not change in time. We then have a simpler expression for the current induced in the coil: The induced current depends on both the area of the coil and the change in magnetic field.

In a coil of wires, each loop contributes an area A to the right-hand side of the equation, so the induced emf will be proportional to the number of loops in a coil. But doubling the number of loops doubles the length of wire used and so doubles the resistance, so the induced current will not increase when loops are added.

Induction and Magnetic Recording A traditional recording head for magnetic data consists of a coil of wires attached to some current-sensitive device. A ferromagnetic material passes under the coil. Such an arrangement can both write magnetic data to the ferromagnetic material and read magnetic data off of the material. To write magnetic data, current is sent through the coil in proportion to the desired signal.

This current produces a magnetic field proportional to the current. The magnetic field aligns the spins in the ferromagnetic material. As the material moves away from the coil, the magnetic field decreases, and the spins remain aligned until they enter another magnetic field when they are erased.

Unlike electric storage, magnetic storage can be either analog or digital. The amount of spin alignment depends on the strength of magnetic field, so analog data can be recorded with a continually varying current producing a continually varying magnetic field. Digital data can be recorded by alternating the direction of the current. To minimize data loss or errors, binary data is not determined solely by the direction of magnitization in a domain.

Instead, it is represented by the change in magnetic orientation between two domains. If one bit of magnetic field has the same direction as the one before it, that represents a 0 no change. If one bit of magnetic field has the opposite direction as the one before it, that represents a 1 change. So a 1 is written by changing the direction of current between the two domains comprising a bit, and a 0 is written by keeping the direction the same.

### Introduction to Magnetism and Induced Currents

Each bit starts with a change of orientation. This convention for recording data identifies errors, since one would never have three domains of the same orientation in a row. In addition, the orientation should change with every other domain. If the computer thinks a bit is complete but the orientation does not change, it knows that some error has occurred.

- Induced current in a wire

Some examples of domains, bits, and strings are shown below. To read magnetic data, the ferromagnetic material is moved past the coil of wire. The changing magnetic field caused by the material's motion induces a current in the coil of wire proportional to the change in field. If a 0 is represented, the magnetic field does not change between the two domains of a bit, so no current is induced as the magnetic material passes the coil.

For a 1, the magnetic field changes from one direction to the other; this change induces a current in the coil.

Inductive reading of magnetic data is subject to many limitations. Since the change in magnetic field will be greater if the ferromagnetic material is moved faster, the induced current is dependent on the speed of the material. Thus the sensitivity of inductive read heads is limited by the precision of the material speed. The other limiting factor on inductive heads is the strength of the magnetic field.

As efforts to increase storage density continue, the size of a data element shrinks. Since fewer electrons are now contained in the region of one bit, the associated magnetic field is smaller. You should notice two things: If the magnet is held stationary near, or even inside, the coil, no current will flow through the coil.

If the magnet is moved, the galvanometer needle will deflect, showing that current is flowing through the coil. When the magnet is moved one way say, into the coilthe needle deflects one way; when the magnet is moved the other way say, out of the coilthe needle deflects the other way.

Not only can a moving magnet cause a current to flow in the coil, the direction of the current depends on how the magnet is moved. How can this be explained? It seems like a constant magnetic field does nothing to the coil, while a changing field causes a current to flow. To confirm this, the magnet can be replaced with a second coil, and a current can be set up in this coil by connecting it to a battery.

The second coil acts just like a bar magnet. When this coil is placed next to the first one, which is still connected to the galvanometer, nothing happens when a steady current passes through the second coil.

When the current in the second coil is switched on or off, or changed in any way, however, the galvanometer responds, indicating that a current is flowing in the first coil. You also notice one more thing. If you squeeze the first coil, changing its area, while it's sitting near a stationary magnet, the galvanometer needle moves, indicating that current is flowing through the coil.

What you can conclude from all these observations is that a changing magnetic field will produce a voltage in a coil, causing a current to flow. To be completely accurate, if the magnetic flux through a coil is changed, a voltage will be produced. This voltage is known as the induced emf. The magnetic flux is a measure of the number of magnetic field lines passing through an area.

If a loop of wire with an area A is in a magnetic field B, the magnetic flux is given by: If the flux changes, an emf will be induced. There are therefore three ways an emf can be induced in a loop: Change the magnetic field Change the area of the loop Change the angle between the field and the loop Faraday's law of induction We'll move from the qualitative investigation of induced emf to the quantitative picture.

As we have learned, an emf can be induced in a coil if the magnetic flux through the coil is changed. It also makes a difference how fast the change is; a quick change induces more emf than a gradual change. This is summarized in Faraday's law of induction.