Magnetic Fields

The three most common magnetic metals are iron, cobalt and nickel.

Magnetic field

This is a region of space where a magnetically susceptible material experiences a force.

The density of the field (flux) lines represents the strength of the field.

The point where the fields cancel out is known as the neutral point.

Finding the north and south ends of a solenoid

North moves outward

South moves inward

Magnetic flux ( \varphi )

Magnetic flux is the number of lines in a region of space within a magnetic field. It is measured in Webers ( Wb).

Magnetic flux density (B)

It is the force produced when a current of 1A flows through a 1m length of wire.

Indicates strength of magnetic field.

Measured in Teslas (T)

B=\frac{\Phi}{A}

where Φ = magnetic flux, A = area

Force on a current carrying wire in a magnetic field

• Current passing through a conductor creates a magnetic field.

• Placing the conductor in an external magnetic field creates a resultant field.

• The resultant field creates a pushing force which causes the wire / conductor to move.

  The above is the motor effect

  F=BIL\sin\theta

where θ is the angle of wire to field

Force is at maximum when current is at right angles to the magnetic field.

Force is at minimum when current is parallel to the magnetic field.

Fleming Left Hand Rule

Current is always conventional.

Force direction is always a positive charge.

If a question is about flow of negative charge, use the rule then swap the direction at the end.

F=BQv\sin\theta

where θ = angle of charge movement to field

Generator effect

• A conductor moves through a magnetic field.

• The magnetic field exerts a force on the electrons in the conductor.

• A current is induced in the conductor.

Electromagnetic Induction

• Electrons in a wire will experience a force whenever the wire cuts magnetic flux lines

• The electrons accumulate on one end of the wire

• This causes difference in charge between the ends of the use and a potential difference is set up

• So, an emf is induced into the wire

Note: no movement of wire or field = no emf

Ways to increase EMF

1. Move the wire or field faster

2. Use a stronger magnet

3. Increase the number of turns of the coil

Flemings Right Hand Rule (used only for induced currents)

Magnetic flux (Φ)

\Phi=BA\cos\theta (for a single loop)

where cosθ = angle of field to normal of plane

Magnetic flux linkage (N\phi )

Magnetic flux of a coil of wire with N turns

N\phi=BAN\cos\theta

where N = number of turns of wire

Faraday's Law of Electromagnetic Induction

A change of flux linkage of 1Wb per second will induce an emf of 1V in a loop of wire

\char"0190 =\frac{\Delta N\phi}{\Delta t}

where ε = induced emf (V)

Lenz's Law

The emf that is induced will be in such a direction as to oppose the charge producing it.

\char"0190 =-\frac{\Delta N\phi}{\Delta t}

If the negative sign wasn't there, the laws of conservation of energy will be violated

Demonstrating Lenz's Law

When you drop a magnet down a copper tube, what happens?

• The copper tube is not magnetic

• The magnet has its own magnetic field

• When the magnet is dropped, an emf is induced and current starts to flow

• The current produces its own magnetic field which is equal and opposite to the magnetic field of the magnet

• Applying Lenz's Law, they exert resistive forces on the magnet, slowing it down

Alternating Currents and Transformers

AC Current

AC current is a current that charges with time in a regular, repetitive manner

Depends on the voltage and resistance of the supply

Has a repeating sine (sinusoidal) waveform

V_{rms}=\frac{V_0}{\sqrt2}

I_{rms}=\frac{I_0}{\sqrt2}

P_{rms}=I_{rms}\times V_{rms}

Transformers

Transformers use electromagnetic induction to change the size of a voltage for an alternating current.

How do transformers work?

Step 1:-

An alternating emf causes an alternating current to flow into the primary coil

This causes the iron core to alternately magnetise and demagnetise

The changing magnetic field is continuously being produced in opposite directions

A DC Current can't do this because the direction isn't changing so flux linkage doesn't change

Step 2:-

Magnetic flux is now rapidly changing

This passes through the secondary coil where it induces an alternating voltage of the same frequency as the input voltage.

Step 3:-

The secondary coil has a different number of turns to the primary cost

The alternating voltage induced is different to the input voltage because:

\frac{V_{p}}{V_{s}}=\frac{N_{p}}{N_{s}}