1. Up4. Left 2. Down5. Into the page 3. Right6. Out of the page (back of card) No Direction ConcepTest #17: A uniform magnetic field B points into the page as shown. A short straight wire (length L ) is moved to the right with speed v. Consider the following directions. Hold up as many cards as you need to specify the direction. a) What direction is the magnetic force acting on the electrons in the wire? b) What direction is the electric field acting in the wire? x x x x x v ℓ What is the magnitude of the electric field in the wire, in steady state? What is the magnitude of the potential difference in the wire?

ConcepTest #18: A uniform magnetic field B points into the page as shown. A piece of conducting wire is bent into a sideways “U” shape. Another piece of short straight wire can slide along the “rails” of the U shape, and is moved to the right speed with speed v. What is the direction of the induced current in the loop? x x x x x v 1. Clockwise 2. Counterclockwise 3. No current 4. Not enough info

Example: Applying Faraday’s Law for Changing Area A uniform magnetic field points into the page as shown. A piece of short straight wire can slide along the “rails” of the U shape, and is moved to the right speed with speed v. What is the magnitude of the induced  in this situation? x x x x x v ℓ x

Example: Applying Faraday’s Law for Changing Angle A circular conducting loop of area 0.1 m 2 has 5 turns and is in a uniform magnetic field of 0.02 T that points in the positive x direction. What is the magnetic flux through the loop at the instant pictured? What happens as the loop rotates about the z axis?

Example: Applying Faraday’s Law for Changing Magnetic Field A uniform magnetic field B is produced in a solenoid of cross sectional area A, as shown. A loop is concentric with the axis of the solenoid, and has radius R. The current in the solenoid varies with time, so the magnetic field in the solenoid also varies with time, such that B ( t ) = B 0 t. What is the magnitude of the induced  in the loop? What is the magnitude of the induced electric field? If the loop were conducting, what direction would the induced current flow? R

Lenz’s Law for determining direction of induced electric field, current Magnetic field increases?

Example: Applying Lenz’s Law – Fight the Flux Change! A solenoid is used to create a uniform magnetic field that points into the page. A wire loop of area A is in the magnetic field, as shown. For each of the following cases, choose one of the following for the direction of the induced current in the loop: x x x x x 1. Clockwise 2. Counterclockwise 3. No current 4. Not enough info a)The loop is moved to the left, staying in the B field. b)The loop is crushed to a smaller area. c)The loop is rotated so that the top of the loop comes out of the page and the bottom of the loop goes into the page. d)The magnetic field is increased. e)The magnetic field direction is reversed.

ConcepTest #19: A long straight wire carries current to the right, as shown. A square loop of wire (with a resistor) is initially stationary below the straight wire. Consider the following directions: 1. Up4. Left 2. Down5. Into the page 3. Right6. Out of the page (back of card) No Direction a) What is the direction of the magnetic field due to the straight wire at the location of the wire loop? b)If the current in the straight wire is decreasing, what is the direction of the induced current in the resistor? c)What direction will the loop move? (Ignore rotations)

ConcepTest #20: A bar magnet is released above a circular loop of wire as shown, and falls through the loop. The loop is held fixed. Consider the following directions, as viewed when looking at the loop from above: a) What is the direction of the induced current in the wire loop, while the bar magnet is falling towards the loop from above? 1. Clockwise 2. Counterclockwise 3. No current 4. Not enough info NSNS NSNS N b) What is the direction of the induced current in the wire loop, while the bar magnet is falling away from the loop from below?

Try it Yourself: A uniform magnetic field points into the page as shown. A disk made out of a conducting material that lies in the plane of the page is rotated clockwise. Is any  induced in the disk? Explain. Try it Yourself: A long straight wire carries current I out of the page as shown, and is surrounded by a circular wire loop of radius a. The current in the straight wire is decreasing. Is any current induced in the circular loop? If so, in what direction? Explain. x x x x x