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Faraday’s Law of Induction
AP Physics C Mrs. Coyle

How can current be induced in a wire?
Michael Faraday English professor A current is induced in a wire, when the magnetic field that is “felt” by the wire is changed.

Induced Current and Induced EMF
An induced current is produced by a changing magnetic field A current can be produced without a battery present in the circuit

Faraday’s Law of Induction
The emf, E induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit”

Note If the circuit consists of N loops, all of the same area, and if FB is the flux through one loop, an emf is induced in every loop

Magnetic Flux θ

Magnetic Flux, F: The number of magnetic (flux) field lines which pass through a given cross-sectional area A Units: F webers B Tesla A area m2 angle formed between B and the normal to the loop (area vector A) The area vector A is perpendicular to the surface A and has a magnitude equal to the area A.

Example The magnetic flux through the loop is FB = BA cos q
The induced emf is e = - d/dt (BA cos q)

The magnetic flux can be changed by:
Changing the orientation of the wire loop in which the current is to be induced (movement). Changing the strength of the magnetic field (change current of wire that causes the field). Changing the area of the coil.

1. Movement When a wire is moved in a constant magnetic field, the wire “feels” a changed magnetic field and current is induced.

1. Change Caused by Movement -Sliding Conducting Bar (Motional EMF)
emf = - B Lv sinq L: length of the wire q: angle between v and B

Sliding Conducting Bar
Induced emf : Induced Current:

Sliding Conducting Bar
A bar moving through a uniform field and the equivalent circuit diagram Assume the bar has zero resistance The work done by the applied force appears as internal energy in the resistor R

Sliding Conducting Bar and Energy
The applied force does work on the conducting bar to move charges through a magnetic field The change in energy of the system during some time interval must be equal to the transfer of energy into the system by work The power input is equal to the rate at which energy is delivered to the resistor

Generator

Generators at Hoover Dam

3 minute video on Hoover Dam

2. Electromagnetic Induction by changing the current causing the B-field (thus changing the B-field).

Changing Magnetic Field

Faraday’s Experiment A primary coil is connected to a switch and a battery The wire is wrapped around an iron ring A secondary coil is also wrapped around the iron ring There is no battery present in the secondary coil The secondary coil is not directly connected to the primary coil

Faraday’s Experiment At the instant the switch is closed, the galvanometer (ammeter) needle deflects in one direction and then returns to zero When the switch is opened, the galvanometer needle deflects in the opposite direction and then returns to zero The galvanometer reads zero when there is a steady current or when there is no current in the primary circuit

Faraday’s Experiment An electric current can be induced in the secondary circuit by changing the magnetic field The induced current exists only while the magnetic field is changing Note: the flux must be changing

The Flying Ring

Question In the “flying ring” demo, how was the magnetic field “felt” by the copper ring changed? Answer: AC current

3. When B is constant and A (area) is changing.

Ways of Inducing an emf The magnitude of B can change with time
The area enclosed by the loop can change with time The angle q between B and the normal to the loop can change with time Any combination of the above can occur

Applications of Faraday’s Law -GFI (Ground Fault Interuptor)
A GFI protects users of electrical appliances against electric shock by triggering a circuit breaker When the currents in the wires are in opposite directions, the flux is zero When the return current in wire 2 changes, the flux is no longer zero An emf results which can be trigger a circuit breaker.

Applications of Faraday’s Law – Pickup Coil of an Electric Guitar
The coil is placed near the vibrating string and causes a portion of the string to become magnetized When the string vibrates at the same frequency, the magnetized segment produces a changing flux through the coil The induced emf is fed to an amplifier

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