Electromagnetic Induction – Learning Outcomes

Define magnetic flux.

Solve problems about magnetic flux.

State Faraday’s Law.

HL: Solve problems using Faraday’s Law.

State Lenz’s Law.

Demonstrate the principles and laws of electromagnetic

induction.

Discuss electromagnetic induction in generators.

Solve problems about converting between mechanical and

electrical energy.

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Electromagnetic Induction Just as a current generates a magnetic field, a

changing magnetic field can induce an e.m.f. in a

conductor (usually we consider a coil).

This effect is called electromagnetic induction.

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Magnetic FluxWhen a magnetic field of magnetic flux density B passes

perpendicular to an area A, the magnetic flux, Φ

passing through the area is given by:

𝜙 = 𝐵𝐴

Magnetic flux is a scalar quantity.

It is measured in weber, Wb.

If the magnetic flux density over an area of 1 m2 is 1 T,

then the magnetic flux through the area is 1 Wb.

Note that if the field passes through a solenoid, the

effective area is proportional to the number of coils.

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Magnetic Flux e.g. What is the magnetic flux through a loop of area 0.4

m2 placed at right angles to a magnetic field of 2 T?

e.g. The magnetic flux passing though a coil of wire is 2 ×10-2 Wb. The field is uniform and perpendicular to the

plane of the coil. The area of the coil is 200 cm2. Find the

flux density at any point in the coil.

e.g. What is the magnetic flux through a loop of area 0.4

m2 in a magnetic field of 2 T if the flux density makes 30o

with the loop?

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Faraday’s Law Faraday’s Law states that the size of the induced emf is

proportional to the rate of change of flux.

Formula: 𝐸 ∝Δ𝜙

𝑡

The constant of proportionality is -1 in this case, so this is

usually written as:

Formula: 𝐸 = −𝑑𝜙

𝑑𝑡

We can ignore the calculus notation.

Note the negative sign indicating the direction of the

induced emf (we don’t need it for calculations).

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Faraday’s Law e.g. The magnetic flux through a loop changes from 2

Wb to 8 Wb in 4 seconds. Find the average emf induced

in the loop.

If the coil has a resistance of 10 Ω, find the induced

current.

e.g. Find the emf induced in a 100 turn coil of wire if the

flux through it changes from 0 Wb to 6Wb in 0.2 s.

e.g. A 100 turn rectangular coil of dimensions 6 cm × 8

cm rotates at constant angular speed in a uniform

magnetic field of flux density 2 T. If the coil undergoes 5

rotations per second, find the average induced emf in

the coil in going from parallel to the field to

perpendicular to the field.

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To Demonstrate Faraday’s Law1. Connect a coil of wire to a galvanometer.

2. Move a bar magnet slowly towards the coil.

3. Note a small deflection in the galvanometer.

4. Move the bar magnet quickly towards the

coil.

5. Note a larger deflection in the galvanometer.

6. The size of the current (and thus, emf)

increases as the speed of the magnet (and

thus rate of change of flux) increases.

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Lenz’s Law Lenz’s Law states that the direction of an induced

current is always such as to oppose the change

producing it.

e.g. if a north pole is brought near a solenoid, the

solenoid will produce a current such that its field has a

north pole repulsing the incoming one.

e.g. if a north pole is moved away from a solenoid, the

solenoid will produce a current such that its field has a

south pole attracting the north pole.

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Lenz’s Law e.g. If the bar magnet is not moving, in which direction

will the current in the solenoid flow?

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Lenz’s Law e.g. If the bar magnet is brought towards the solenoid, in

which direction will the current flow?

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Lenz’s Law e.g. If the bar magnet is moved away from the solenoid,

in which direction will the current flow?

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To Demonstrate Lenz’s Law1. Suspend a ring of aluminium from a length of string.

2. Move one pole of a bar magnet quickly towards the

ring.

3. Note that the ring is repelled.

4. Move the magnet quickly away from the ring.

5. Note that the ring is pulled along with the magnet.

6. When the ring is repelled, the induced current creates a

pole the same as the approaching one on that side.

7. When the ring is attracted, the induced current creates

a pole opposite the leaving one on that side.

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To Demonstrate Lenz’s Law13

Generators An electric generator is a device that converts

mechanical energy to electrical energy.

Generators use the principles of electromagnetic

induction to perform this conversion.

In most cases, chemical energy (coal, oil, biomass,

nuclear) is burned for heat, producing steam which

drives a turbine. Wind, hydroelectric, tidal harvest kinetic

energy to drive the turbine.

Turbines consist of a coil which can rotate in a magnetic

field, inducing an emf.

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GeneratorsGenerators appear in:

Electricity power stations – as described earlier.

Car alternators – convert rotation in the engine to

electricity to supply the car’s electrical system and

charge the battery.

Bicycle dynamos harvest the bicycle’s kinetic energy to

operate the lights.

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GeneratorsWe examine the simple situation of a magnet moving

towards a coil of wire.

If the resistance of the coil is 5 Ω and the induced current

is 0.2 A, find the force on the magnet if it moves towards

the coil at 10 m s-1.

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Hint: Conservation

of energy tells us

that the work done

by the magnet is

equal to the heat

produced in the

coil.

Generators e.g. If the resistance of a coil is 20 Ω and the induced

current is 0.6 A, find the force on the magnet if it moves

towards the coil at 30 m s-1.

e.g. A rectangular coil of one turn and dimensions 5 cm

× 12 cm enters a uniform magnetic field of flux density 2

T which is perpendicular to the plane of the coil. If the

coil moves at 4 m s-1 parallel to the 12 cm side and has a

resistance of 5 Ω, find:

i. the emf induced in the coil,

ii. the force that must be exerted on the coil to keep it

moving at that speed.

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