# Introduction a potential difference (voltage) across a conductor

Introduction

It was first discovered that current in a wire produces a magnetic field and

then Michael Faraday discovered that the opposite is also true in that a

magnetic field can produce a current inside a conductor.

Electromagnetic Induction is the production of a potential difference (voltage)

across a conductor when it is exposed to a changing magnetic field. When a

conductor is moved across a magnetic field so as to cut through the lines of

magnetic flux, an electromotive force (emf) is produced in the conductor. Magnetic

flux is how any material is affected by a magnetic field. The moving magnetic

field caused by the changing magnetic flux induces emf however the measure of

magnetic flux is not important, it is whether or not there’s change in flux

over time.

If the conductor forms part of a closed circuit then the emf produced causes electrons

to flow round the circuit thus a current is produced.

When a magnetic field associated with a magnet, moves towards a coil of wire,

the magnetic flux of the magnet moves across or cuts the coil. It is the

relative movement of the magnetic flux and the coil that causes an emf and thus

current to be induced in the coil.

·

When the magnet is moved at a constant speed

towards and/or through the coil, the galvanometer moves showing that current

has been produced in the coil.

·

When the magnet is moved at the same speed as

before but away from the coil, the same movement on the galvanometer is seen but

in the opposite direction.

·

When the magnet is motionless, even within the

coil, the galvanometer does not move.

·

When the coil is moved rather than the magnet at

the same speed as before and the magnet is held stationary, it results in the

same galvanometer measurement as before.

·

When either the speed of the magnet or coil is

doubled whilst the other is stationary, it results in a doubled galvanometer

measurement.

·

When a stronger magnet is used, it results in a

greater measurement.

·

When the number of turns of wire of the coil is

increased, it results in a greater measurement.

Laws

Faraday’s First Law: Any change

in the magnetic field of a coil of wire will cause an emf to be induced in the

coil. With this induced emf if the conductor circuit is closed, current will

also circulate through the circuit and this current is called induced current.

Faraday’s Second Law: The magnitude

of emf induced in the coil is equal to the rate of change of flux that links

with the coil. The flux linkage of the coil is the product of number of turns

in the coil and flux associated with the coil.

Lenz’s Law: An electric current,

induced by a source such as a changing magnetic field, always creates a

counterforce opposing the force inducing it.

Fleming’s Hand Rules: Used to aid in

the understanding of magnetic field, motion and induced current directions. Fleming’s

left-hand rule is used for electric motors, while Fleming’s right-hand rule is

used for electric generators. Different hands need to be used for motors and

generators because of the differences between cause and effect. In an electric

motor, the electric current and magnetic field exist (which are the causes),

and they lead to the force that creates the motion (which is the effect).

Applications

Electromagnetic induction is the fundamental operating principles of

transformers, inductors and many types of electrical motors, generators and

solenoids:

In an electric motor, the motor has coils turning inside magnetic fields, and a

coil turning inside a magnetic field induces an emf. This emf, known as the

back emf, acts against the applied voltage that’s causing the motor to spin in

the first place, and reduces the current flowing through the coils.

In AC generators, conductors forming an electric circuit are made to move

through a magnetic field. By Faraday’s law an emf is induced in the conductors

and thus a source of emf is created. A generator convert mechanical energy into

electrical energy.

In a transformer, alternating current from primary coil moves quickly back and

forth across the secondary coil. The moving magnetic field caused by the

changing flux induces a current in the secondary coil, stepping the voltage

either up or down.

Formulae

The image above shows a conductor moving backwards and forth between a magnet.

The formula used to calculate induced emf is:

E = Blv (measured

in volts).

B is the flux density measured in tesla, l is the length of the conductor

measured in metres and v is the conductor velocity measured in metres per

second.

The equation above assumes the conductor moves through the magnetic field at a

90?

however when the conductor moves through at an angle ??, the equation is:

E = Blv sin?

The first equation is for a linear conductor. There are also loop conductors where

total emf is doubled, 2Blv sin?. If the loop has numerous turns it is now a

coil and the number of turns in the coil, N, must be considered in the equation,

therefore the total emf for a loop conductor is:

E = 2NBlv sin?

Inductance

Before examining inductance, firstly Inductors must be discussed. An

inductors is a components used when the property of inductance is required in a

circuit and it is basically a coil of wire. Inductance can be thought of as the

change in current and flux linkages that induces emf in a circuit. There are

two types of inductance, self and mutual inductance. Self inductance is when

the emf is induced in the same circuit as that in which there is a change of

flux due to current change and mutual inductance is when emf is induced in a

circuit but the change in flux due to current change is in an adjacent circuit.

The equations for measuring induced emf in a coil of N turns is:

The change in flux, measured in webers in d? and dt is the time

taken for the flux to change in seconds.

Taking current into account to actually find the inductance of a coil is given

by:

Where L is inductance measured in Henry, change in flux, measured in webers, d? = ? and I is

current measured in amperes. Putting those two equations together results in:

Where dI is change in current and dt is the time taken for the current to

change.

The minus sign in the induced emf equations represents the direction of emf

given by Lenz’s Law.

Going back to inductors, there are a number of factors that affect the inductance

of an inductor including:

·

Number of turns in a wire – more turns more

inductance.

·

Arrangement of turns – the shorter and thicker

the coil of wire, the higher the inductance.

·

Cross-sectional area of the coil of wire – the greater

the area, the higher the inductance.

·

Presence of a magnetic core in the wire

An inductor can store energy,

measured in joules, in its magnetic field and to calculate it, the formula is:

Another aspect to consider when calculating inductance is Reluctance which is

the magnetic resistance of a magnetic circuit to the presence of magnetic flux,

however it is not necessary to know at this point in the understanding of

electromagnetic induction.