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Chapter 34. Electromagnetic Induction

Electromagnetic induction is the scientific principle that underlies many modern technologies, from the generation of electricity to communications and data storage.

Chapter Goal: To understand and apply electromagnetic induction.

Chapter 34. Electromagnetic Induction

Topics:

- Induced Currents
- Motional emf
- Magnetic Flux
- Lenz’s Law
- Faraday’s Law
- Induced Fields
- Induced Currents: Three Applications
- Inductors
- LC Circuits
- LR Circuits

Currents circulate in a piece of metal that is pulled through a magnetic field. What are these currents called?

- Induced currents
- Displacement currents
- Faraday’s currents
- Eddy currents
- This topic is not covered in Chapter 34.

Currents circulate in a piece of metal that is pulled through a magnetic field. What are these currents called?

- Induced currents
- Displacement currents
- Faraday’s currents
- Eddy currents
- This topic is not covered in Chapter 34.

Electromagnetic induction was discovered by

- Faraday.
- Henry.
- Maxwell.
- Both Faraday and Henry.
- All three.

Electromagnetic induction was discovered by

- Faraday.
- Henry.
- Maxwell.
- Both Faraday and Henry.
- All three.

The direction that an induced current flows in a circuit is given by

- Faraday’s law.
- Lenz’s law.
- Henry’s law.
- Hertz’s law.
- Maxwell’s law.

The direction that an induced current flows in a circuit is given by

- Faraday’s law.
- Lenz’s law.
- Henry’s law.
- Hertz’s law.
- Maxwell’s law.

Faraday’s Discovery

Faraday found that there is a current in a coil of wire if and only if the magnetic field passing through the coil is changing. This is an informal statement of Faraday’s law.

Magnetic data storage encodes information in a pattern of alternating magnetic fields. When these fields move past a small pick-up coil, the changing magnetic field creates an induced current in the coil. This current is amplified into a sequence of voltage pulses that represent the 0s and 1s of digital data.

Motional emf

The motional emf of a conductor of length l moving with velocity v perpendicular to a magnetic field B is

Magnetic Flux

The magnetic flux measures the amount of magnetic field passing through a loop of area A if the loop is tilted at an angle θ from the field, B. As a dot-product, the equation becomes:

Lenz’s Law

There is an induced current in a closed, conducting loop if and only if the magnetic flux through the loop is changing. The direction of the induced current is such that the induced magnetic field opposes the change in the flux.

Faraday’s Law

An emf is induced in a conducting loop if the magnetic flux through the loop changes. The magnitude of the emf is

and the direction of the emf is such as to drive an induced current in the direction

given by Lenz’s law.

Inductance of a solenoid

The inductance of a solenoid having N turns, length l and cross-section area A is

The potential difference across an inductor

The potential difference across an inductor with an inductance of L and carrying a current I is

The current in an LC circuit

The current in an LC circuit where the initial charge on the capacitor is Q0 is

The oscillation frequency is given by

EXAMPLE 34.15 An AM radio oscillator

QUESTION:

A square conductor moves through a uniform magnetic field. Which of the figures shows the correct charge distribution on the conductor?

A square conductor moves through a uniform magnetic field. Which of the figures shows the correct charge distribution on the conductor?

Is there an induced current in this circuit? If so, what is its direction?

- No
- Yes, clockwise
- Yes, counterclockwise

Is there an induced current in this circuit? If so, what is its direction?

- No
- Yes, clockwise
- Yes, counterclockwise

A square loop of copper wire is pulled through a region of magnetic field. Rank in order, from strongest to weakest, the pulling forces Fa, Fb, Fc and Fd that must be applied to keep the loop moving at constant speed.

- Fb = Fd > Fa = Fc
- Fc > Fb = Fd > Fa
- Fc > Fd > Fb > Fa
- Fd > Fb > Fa = Fc
- Fd > Fc > Fb > Fa

A square loop of copper wire is pulled through a region of magnetic field. Rank in order, from strongest to weakest, the pulling forces Fa, Fb, Fc and Fd that must be applied to keep the loop moving at constant speed.

- Fb = Fd > Fa = Fc
- Fc > Fb = Fd > Fa
- Fc > Fd > Fb > Fa
- Fd > Fb > Fa = Fc
- Fd > Fc > Fb > Fa

A current-carrying wire is pulled away from a conducting loop in the direction shown. As the wire is moving, is there a cw current around the loop, a ccw current or no current?

- There is no current around the loop.
- There is a clockwise current around the loop.
- There is a counterclockwise current around the loop.

A current-carrying wire is pulled away from a conducting loop in the direction shown. As the wire is moving, is there a cw current around the loop, a ccw current or no current?

- There is no current around the loop.
- There is a clockwise current around the loop.
- There is a counterclockwise current around the loop.

A conducting loop is halfway into a magnetic field. Suppose the magnetic field begins to increase rapidly in strength. What happens to the loop?

- The loop is pulled to the left, into the magnetic field.
- The loop is pushed to the right, out of the magnetic field.
- The loop is pushed upward, toward the top of the page.
- The loop is pushed downward, toward the bottom of the page.
- The tension is the wires increases but the loop does not move.

A conducting loop is halfway into a magnetic field. Suppose the magnetic field begins to increase rapidly in strength. What happens to the loop?

- The loop is pulled to the left, into the magnetic field.
- The loop is pushed to the right, out of the magnetic field.
- The loop is pushed upward, toward the top of the page.
- The loop is pushed downward, toward the bottom of the page.
- The tension is the wires increases but the loop does not move.

The potential at a is higher than the potential at b. Which of the following statements about the inductor current I could be true?

- I is from b to a and is steady.
- I is from b to a and is increasing.
- I is from a to b and is steady.
- I is from a to b and is increasing.
- I is from a to b and is decreasing.

The potential at a is higher than the potential at b. Which of the following statements about the inductor current I could be true?

- I is from b to a and is steady.
- I is from b to a and is increasing.
- I is from a to b and is steady.
- I is from a to b and is increasing.
- I is from a to b and is decreasing.

Rank in order, from largest to smallest, the time constants τa, τb, and τc of these three circuits.

- τa > τb > τc
- τb > τa > τc
- τb > τc > τa
- τc > τa > τb
- τc > τb > τa

Rank in order, from largest to smallest, the time constants τa, τb, and τc of these three circuits.

- τa > τb > τc
- τb > τa > τc
- τb > τc > τa
- τc > τa > τb
- τc > τb > τa

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