# Unit 4: Section 4 - Magnetic Fields

Notes from A2 AQA physics book

## Magnetic Fields

Magnetic fields can be represented by field lines. These lines goes from north to south. The closer the lines are together, the stronger the field.

When current is passed through a wire a magnetic field is induced around the wire. The field lines in this system are concentric circles centred on the wire. The direction of the magnetic field around the current carrying wire can be worked out using the right hand rule.

If the wire is a wrapped into a coil then the field will be a doughnut shape. however if there are a lot of coils, then the field will be like a bar magnets.

Right Hand Rule - Put your hand into the shape you'd make if you was hitching and point your thumb in the direction of the current. The direction your curled fingers are pointing is the direction of the magnetic field.

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## Magnetic Fields Cont.

If you put a current carrying wire into an external magnetic field ( EG. between two magnets ) the field around the wire and the field from the magnet interact. The field lines from the magnet contract to form a "stretched catapult" effect where the flux lines are closer together.

This causes a force on the wire. However if the current in the wire is parallel to the flux lines then no force acts. The direction of the force is always perpendicular to both the current direction and the magnetic field. This is shown by Fleming's left hand rule:

Make a "gun" shape with your thumb and first finger, and hold your second finger at a right angle to your first.

Thumb - The direction of the Force ( Where motion takes place )

First finger - The direction of the uniform magnetic field

Second finger - The direction of the conventional current

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## Magnetic Fields Cont.

The force on a wire is proportional to the magnetic field strength.

F = B x I x L

B is the magnetic field strength, I is the current and L is the length of wire within the field.

The magnetic field strength is also called the flux density and is measured in teslas, T.

1 tesla = Wb / m²

Flux density - The number of flux lines per unit area

The electric current in a wire is caused by the flow of negatively charged electrons.

Current, I is the flow of charge, q in time t. q = it

A charged partical moves a distance, l in time t has a velocity, v = l / t

By putting these equations together you get, F = Bqv

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## Magnetic Fields Cont.

Based on fleming's left hand rule, the force on a moving charge in a magnetic field is always perpendicular to its direction of travel.

Mathematically, that is the condition for circular motion.

This effect is used in particle accelerators which use magnetic fields to accelerate particles to very high energies along circular paths.

The radius of curvature of the path of a charged particle moving through a magnetic field gives you information about the particle's charge and mass. This means you can identify different particles by studying how they're deflected.

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## Electromagnetic Induction

The total magnetic flux, φ, passing through an area, A, perpendicular to a magnetic field, B is defined as:

φ = BA

When a coil is moved into a magnetic field, the size of the e.m.f. induced depends on the magnetic flux passing through the coil φ and the number of turns on the coil. The product is called the flux linkage, Φ

Φ = Nφ = BAN

If the magnetic flux is not perpendicular to B then:

Φ = BA cos θ

Where θ is the angle between the field and the normal to the plane of the coil

For a coil of N turns, the flux linkage is: Φ = BAN cos θ

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## Electromagnetic Induction Cont.

If a conducting rod moves through a magnetic field its electrons will accumulate at one end of the rod due to the force it experiences due to the magnetic field.

The creates an e.m.f. across the ends of the rod.

If the rod is part of a complete circuit, then an induced current will flow through. This is called electromagnetic induction.

An e.m.f(electromotive force) is induced when there is a relative motion between a conductor and a magnet. If either the conductor or the field move while the other one stays still you will get an e.m.f.

Flux cutting always induces e.m.f but will also induce a current if the circuit is complete.

Flux linking is when an e.m.f is induced by changing the magnitude or direction of the magnetic flux. This can be done by using an alternating current electromagnet

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## Electromagnetic Induction Cont.

Faraday's Law: he induced e.m.f is directly proportional to the rate of change of flux linkage.

Induced e.m.f = flux change / time taken = N φ / t

The size of the e.m.f is shown by the gradient of a graph of φ - t. The area under this graph is the flux change.

Lenz's Law: The induced e.m.f is always in such a direction as to oppose the change that caused it.

By combining these two laws you get a formula that works for both:

Induced e.m.f = - N φ / t

The minus sign shows the direction of the induced e.m.f

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## Electromagnetic Induction Cont.

Lenz's law can be used to find the direction of an induced e.m.f and current in a conductor travelling at right angles to a magnetic field.

1) Lenz's law says that the induced e.m.f will produce a force that opposes the motion of the conductor, a resistance

2) Using fleming's left hand rule by pointing your thumb in the direction of the resistance, you can see which is the opposite direction to the motion of the conductor

3) Your second finger will then give the direction of the induced e.m.f

4) If the conductor is connected as part of a circuit, a current will be induced in the same direction as the induced e.m.f

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