Magnetism #2Induced EMFCh.20

Faraday’s Law of InductionWe now know that a current carrying wire will produce its own magnetic field with the lines in a

pattern.

But, can a magnetic field induce a current?

Magnetic Flux ()Magnetic Flux () is a measure of the amount of

entering perpendicular to a given area (A).

Magnetic Flux is calculated by:

Units are:

The perimeter of the area is usually defined by a “ ” of wire (not necessarily circular). If the magnetic field enters the area at an angle other than , then the formula adjusts to:

Where is the angle between the

Induced EMF ()The goal is to produce a in the wire loop. This is achieved by inducing an voltage. One way is to change the strength (B), and the other is to change the .

The magnetic flux through the loop must change to induce an EMF, and this will produce a current.

Faraday’s Law:

The instantaneous EMF (Voltage) induced in a circuit (with N loops), equals the rate of change of the magnetic flux through the circuit.

=

depends on what is actually changing.

The minus sign indicates the of the induced EMF. It can then be applied to law to solve for the induced current. i.e

Example:A magnet moves away from a wire coil with 25 loops and a radius of 15cm. The perpendicular magnetic field decreases from 1.25T to 0.34T in 4.2s. (a) What is the induced EMF in the coil?

(b) If the coil is attached to a 12 resistor, then what will be the magnitude induced current in the circuit?

Example:

A wire loop with a radius of 5cm and has 50 turns rotates in a magnetic field of 1.2T. It makes 1 complete rotation every 2 seconds. What is the EMF induced in the coil.

Lenz’s Law“An induced current always flows in a direction that produces a magnetic field that the change that caused it”

In this example, the magnet moves to the right increasing the magnetic field (and flux) through the inside of the loop. The current will move in a direction such that it will produce

Motional EMF

Consider 2 parallel metallic rails separated by a distance L, and connected by a wire with a resistor. There is a magnetic field surrounding this set up. Now, lay a metal rod perpendicularly on the rails and slide it.

This effectively changes the over time which induces an

Example:

The diagram below shows a zero resistance rod sliding to the right on two zero resistance rails separated by a distance of 0.45m. The rails are connected by a 12.5 resistor, and the entire system is in a uniform magnetic field with a magnitude of 0.75T. If the velocity of the bar is 5.0m/s to the right, then:

a.) What is the induced EMF.

b.) what is the induced current,

c.) what is the direction of the current, and

d.) what is the magnetic force on the bar?