PHYS 012A Lecture Notes - Lecture 22: Ammeter, Residual-Current Device, String Vibration

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12 Jun 2018

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Chapter 31: Faraday’s Law

EMF Produced by a Changing Magnetic Field

EMF Produced by a Changing Magnetic Field, Summary

- The ammeter deflects when the magnet is moving toward or away from the loop.

- The ammeter also deflects when the loop is moved toward or away from the magnet.

- Therefore, the loop detects that the magnet is moving relative to it.

o We relate this detection to a change in the magnetic field.

o This is the induced current that is produced by an induced emf.

Farada’s Eperiet

- Findings: at the instant the switch is closed, ammeter changes from zero in one direction and then

returns to zero. When the switch is opened, the ammeter changes in the opposite direction and

returns to zero. The ammeter reads zero when there is a steady current or when there is no

current in the primary circuit.

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- Conclusions:

o An electric current can be induced in a loop by a changing magnetic field

▪ this would be the current in the secondary circuit of this experimental set-up

▪ The induced current exists only while the magnetic field through the loop is

changing

o This is expressed as: an induced emf is produced in the loop by the changing magnetic

field

▪ the actual existence of the magnetic flux is not sufficient to produce the induced

emf, the flux must be changing.

- Statements

o Emf is proportional to the time rate of change of the magnetic flux through the circuit

Induced fields

- Magnetic fields vary in time

- An induced current is produced by a changing magnetic field.

- There is an induced emf associated with the induced current.

- A current can be produced without a battery present in the circuit.

- Farada’s la of idutio desries the idued ef.

Farada’s La: Eaple

- Flux through the loop is

Ways of Inducing an emf

- The magnitude of the magnetic field can change with time.

- The area enclosed by the loop can change with time.

- The angle between the magnetic field and the normal to the loop can change with time.

- Any combination of the above can occur.

Appliatios of Farada’s La - GFCI

- GFCI – (ground fault circuit interrupter) protects users of electrical appliances against electric

shock

- When the currents are opposite, flux is zero

- When the return current in wire 2 changes, the flux is no longer zero.

- Resulting induced emf can trigger a circuit breaker

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Related Questions

1a) Faraday discovered that a current is induced in a coil

A) only when the N pole of a magnet is inside the coil
B) only when the S pole of a magnet is inside the coil
C) only when there is a magnetic field inside the coil
D) only when the magnetic field inside the coil is changing

1b). A conductor moves through a uniform magnetic field at speed v and has a motional emf V created across it. If the conductor were to move twice as fast through the magnetic field, the motional emf would be:

A) V
B) 2V
C) 4V
D) V/2
E) V/4

1c) In the conducting rail discussed in section 25.2 (where the rail is moving at constant speed), what can you say about the power input due to the person pulling on the rail and the power dissipated in the resistance?

A) Power input from pull = power dissipated in R
B) Power input from pull > power dissipated in R
C) Power input from pull < power dissipated in R

1d) The electric generator as shown in the reading generates electricity by:

A) rotating a loop inside a magnetic field
B) moving a magnet in and out of a loop
C) sliding a loop over a magnet
D) running current through a loop in a magnetic field

1e) The magnetic flux through a loop:

A) is proportional to the number of magnetic field lines going through it
B) depends just on the B field going through the loop
C) is maximized when the B field lines in the plane of the loop
D) is zero when the B field is perpendicular to the plane of the loop
E) doesn't depend on the direction of the B field

1f) According to Lenz's Law, the induced B field (due to the induced current) will:

A) be in the opposite direction of the existing B field
B) be in the same direction as the existing B field
C) be in the same direction as the change in the existing B field
D) be in the opposite direction of the change in the existing B field

1g) A stationary coil experiences a doubling of its magnetic field (no change in direction of the field) in a time T and has a given induced EMF. If the same change were to have happened in half the time (T/2), the induced EMF would have been:

A) half as large
B) the same
C) twice as large
D) one-fourth as large
E) four times as large

1h) Eddy currents:

A) make it hard to pull a nonmagnetic material through a magnetic field
B) make it hard to pull a magnetic material through a magnetic field
C) speed up a magnetic material moving through a magnetic field
D) speed up a nonmagnetic material moving through a magnetic field