Advanced Higher Physics Unit 2

Electromagnetism

Magnetic Field

A current carrying conductor exerts a magnetic field.The strength of this field is measured by magnetic induction (B).The unit of magnetic induction is the Tesla (T).

The magnetic field around a wire is circular and the direction ofthe field is found using the left hand rule.

IB

Relationship between force exerted on a conductor in a magnetic field and the current in the magnetic field.

Magnetic field and force

If a current carrying conductor is inside a magnetic field then it experiences a force.

l

IB

F=BIlsinθ

θWhere:•B is the magnetic induction in Tesla (T)•l is the length of wire inside the field•Θ is the angle between the field andthe conductor.

Note:•The force is a maximum when the conductor is perpendicular to the field(θ=90˚)•The force is 0 when the conductor is parallel to the field (θ=0˚).

In data booklet

Definition of the tesla

From, the tesla can be defined as:

the magnetic induction (B=1T), of a magnetic field in which aconductor of length one metre (l=1m), carrying a current of oneAmpere (I=1A) perpendicular to the field (θ=90˚,sin 90=0)is acted by a force of one Newton (F=1N).

sinIl

FB

Right hand rule

I

B

F

Example

A wire is suspended from a balance between the poles of a strongmagnet of magnetic induction 84mT. The balance is set to 0. A current of 2.1 A is passed through the wire and the reading on the balance is 11mN.

a) Calculate the angle between the Conductor and the magnetic field.b) State the direction of the force on theWire.c) How can the wire be arranged to increase the force on it to a maximum?d) Calculate the maximum force on theconductor using the same current.e) What happens to the force on the wire when the direction of the 2.1 A current isreversed?

The Hall effect

I

B

F

VHall Voltage

Magnetic induction along a straight wire

Magnetic Field due to an ‘infinite’ conductor

IB

rB

1

r

IkB

When current passes:

r

IB

2

0 170 104 TmA

So

with

[permeability of free space]

In data booklet

Example

Determine the magnetic induction at a distance of 0.25 m from a wire carrying a current of 3.0 A. State any assumption made.

Force between two wires

r

IB

2

101

r

lIIF

2210

I1 I2

rwire 1 wire 2

B1

Wire 1 sets up a magnetic field:

Wire 2 is in this magnetic field and experiencesa force: F=B1I2lUsing right hand rule gives direction of force.

Now substituting gives:

Using left hand rule, gives direction of magneticField B1.

Therefore:r

II

l

F

2210

F

In data booklet

You need to be able to derive this !

By a similar argument it is easy to show that wire 1 experiences thesame force per unit length.

Note:

•If the currents are in the same direction then the force is attractive.

•If the currents are in opposite direction then the force is repelling.

ExampleA long straight conductor has a current of 3.0 A. This conductor is placed parallel to a short straight conductor of length 0.2 m which has a current of 2.5 A. The separation of the conductors is 0.15 m.

1. Calculate the magnetic induction, due to the long conductor, at midpoint M of the short conductor.

2. Calculate the approximate value for the force on the short conductor.

3. Why is this an approximate value for the force?