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### Magnetism

AP Physics B Chapter 21 Notes

What is E/M Induction?

Electromagnetic Induction is the process of using magnetic fields to produce voltage, and in a complete circuit, a current.

Michael Faraday first discovered this by wondering if a moving current created a magnetic field, could a magnetic field create a current?

Induced EMF

He tried unsuccessfully to get emf from a number of set-ups—all involving creating a static B, such as this one.

He did note the galvonometer spiked when he opened or close the switch at X!

Induced EMF

He concluded that only a changing magnetic field produced an emf (induced emf)

Only relative motion is required—either coil or B move

Magnetic Flux

What really drives emf is changing magnetic flux—the dot product of B and area

Flux is proportional to the number of field lines going through a fixed area

Magnetic Flux

Magnetic flux for a uniform magnetic field through a loop of area A is the dot product:

Units: Tm2=Wb (Weber)

Flux changes as a coil rotate in a uniform B—this will induce emf

Changing Magnetic Flux

So how can magnetic flux be changed?

- Change magnetic field strength
- Change area of loop
- Change the angle of the loop of wire to the magnetic field by rotating it

If we do this all quickly, we can get induced emf and current.

Faraday’s Law

Faraday completed many investigations on all of these and derived one of the basic laws of electromagnetism:

What’s with the negative sign?

One Loop

N Loops

Lenz’s Law

Lenz\'s law gives the direction of the induced emf and current resulting from electromagnetic induction--the induced emf and the change in flux have opposite signs.

Lenz’s Law

Lenz’s Law—Practice Problems

Determine the direction of induced current in each case.

Faraday’s and Lenz’s Laws—Example

A coil of wire consists of 20 turns each of which has an area of 0.0015 m2. A magnetic field is perpendicular to the surface. Initially, the magnitude of the magnetic field is 0.050 T and 0.10 s later, it has increased to 0.060 T.

Find the average emf induced in the coil during this time.

Lenz’s Law Summary

Lenz’s Law Reasoning Strategy

1. Determine whether the magnetic flux that penetrates the coil is increasing or decreasing.

2. Find what the direction of the induced magnetic field must be so that it can oppose the change in flux by adding or subtracting from the original field.

3. Use RHR-2 to determine the direction of the induced current.

EMF Induced in a Moving Conductor

What if a conductor is moved in a magnetic field as shown below? The area of the loop increases by

ΔA = LΔx = LvΔt

EMF Induced in a Moving Conductor

Another way to consider what happens is to look at the force acting on an e in the rod:

Motional EMF--Example

Suppose the rod is moving with a speed of 5.0 m/s perpendicular to a 0.80-T magnetic field. The rod has a length of 1.6 m and a negligible electrical resistance. The rails also have a negligible electrical resistance. The light bulb has a resistance of 96 ohms. Find (a) the emfproduced by the rod, (b) the current induced in the circuit, (c ) the electric power delivered to the bulb, and (d) the energy used by the bulb in 60.0 s.

Changing B Flux and Electric Field

Changing magnetic flux produces an induced current which implies an E field in the wire since electrons move. It is found by:

E= F/q = qvB/q = vB

Applications--Generator

An electric generator is the opposite of an electric motor—it converts mechanical energy into electrical energy. AC here.

The axle is rotated by an external force such as falling water or steam. The brushes are in constant electrical contact with the slip rings.

Applications--Generator

DC generators are the same except they have a split ring commutator

Applications--Microphone

Microphones use the same principle to convert sound pressure into electrical signal

Sound pressure moves a diaphragm which is connected to a coil of wire in a magnetic field – the moving coil generates an electrical signal with the same frequency response

Applications--Transformers

A transformer consists of two coils, linked by an iron core. A changing emf in one induces an emf in the other.

Transformers allow emf to be increased or decreased, but require changing current to work—only work for AC

Applications--Transformers

The ratio of emf’s is equal to the ratio of number of coils

Energy is conserved, so the ratio of currents must be the inverse of the ratio of turns

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