Whiteboard Challenge! I II In the scenarios shown above, two identical magnets are held near two identical loops of conducting wire. In case I, the magnet is held a distance x from the loop, and in case II, is held a distance 2x from the loop. Which of the following is true? (A)In case I, the wire will have twice the induced current as in case II. (B)In case II, the wire will have twice the induced current as in case I. (C)In case I, the wire will have a greater induced current, but not twice as great. (D)In case II, the wire will have a greater induced current, but not twice as great. (E)Neither wire will have any current induced in it.

Whiteboard Challenge! I II (A)In case I, the wire will have twice the induced current as in case II. (B)In case II, the wire will have twice the induced current as in case I. (C)In case I, the wire will have a greater induced current, but not twice as great. (D)In case II, the wire will have a greater induced current, but not twice as great. (E)Neither wire will have any current induced in it. Current is caused by a change in magnetic flux! There is no change in flux in either case!

v vv Motional EMF Whiteboard A rectangular loop of wire is made to move at a constant velocity into, through, and out of the magnetic field shown below. Determine the direction of the induced current in the loop a)as the cart is entering the field b)as the cart travels through the field c)as the cart is leaving the field

vvv I: CWI: CCWI: Zero No change in magnetic flux

vvv I I Round II! What will be the direction of the net magnetic force exerted the cart at each of the points shown? Hint: You will need to use RHR #2 for each segment of current-carrying wire that is in the B-field

vvv FBFB FBFB The net magnetic force will oppose the loop of wire entering the field, and then oppose the loop of wire leaving the field! There is zero net magnetic force while the cart is completely within the B field. You will have to push the cart into the field, then let it glide through the field, and finally you have to pull it out!

Coils with Multiple Loops! Each coil acts as its own loop. If there are N coils, Just multiply by N!

Solenoid Φ = N * BA

Solenoids are useful! They multiply the magnetic flux, and therefore the induced emf, by the number of turns that the wire has

Ring Launcher! I

I B coil

This induces a current in the ring that opposes the field of the coil I B coil XSXS XSXS XSXS XSXS B ring I induced

I The current-carrying coil of wire acts like a magnet, with the field lines coming out of North and into South. N S

XSXS XSXS XSXS XSXS B ring I induced XSXS XSXS XSXS XSXS N S The current-carrying ring also acts like a magnet, with the field lines coming out of North and into South.

XSXS XSXS The net result looks like this! I B coil XSXS XSXS XSXS XSXS B ring I induced N S XSXS XSXS N S

Strong repulsion!!! I I induced N S N S

Whiteboard: Copper Tube Drop! N S v a) What will be the direction of the induced current in each of these sections of copper tube? b) Draw the “magnet” that each of these sections acts like. c) What will be the result when the magnet is dropped down the tube?

v Φ: Downward ΔΦ: Upward B induced : Downward Φ: Downward ΔΦ: Upward B induced : Downward I ind Φ: Downward ΔΦ: Downward B induced : Upward Φ: Downward ΔΦ: Downward B induced : Upward I ind

vv

v Attracted by the induced magnet above Repelled from the induced magnet below The magnet will fall slowly!!!

A square loop of wire of resistance R and side a is oriented with its plane perpendicular to a magnetic field B, as shown above. What must be the rate of change of the magnetic field in order to produce a current I in the loop? (A) IR/a 2 (B) Ia 2 /R (C) Ia/R (D) Ra/I (E) IRa

A neutral loop of conducting wire is moved through a uniform magnetic field as shown below. What will happen as a result? v B (A) A clockwise current will flow around the loop (B) A counterclockwise current will flow around the loop (C) The top of the loop will become positively charged and the bottom of the loop will become negatively charged. (D) The top of the loop will become negatively charged and the bottom of the loop will become positively charged. (E) None of the above.

v B Since it is a conductor, we know that the electrons are mobile. Since the electrons are moving to the right in the B-field, we can use RHR # 2 to determine that… The electrons within the conductor will feel an upward force!

v B They will flow to the top of the conductor, giving it a net negative charge. This will leave the bottom of the conductor with a net positive charge.

Quest Today: Magnetism and EM Induction 1. Magnetic field of a current-carrying wire RHR #1 B = (μ 0 I)/(2πr) Superposition of fields 2. Magnetic force felt by a particle and wire RHR #2 F B = qvBsinθ F B = BILsinθ Force exerted between two wires

Test Tomorrow: Magnetism and EM Induction 4. Circular motion in a B-field r = (mv)/(qB) W B = 0 J 5. Crossed E and B fields v undeflected = E/B What happens if too slow, too fast. 3. Determining the direction of the B field, given the force, charge and velocity.

Test Tomorrow: Magnetism and EM Induction 7.Lenz’s Law What causes an induced current? RHR #3 Direction of B induced, I induced 8.Faraday’s Law |ε induced | = |ΔΦ/Δt| 6.Magnetic flux Conceptually Φ = BAcosθ

9. Motional emf |ε induced | = Blv 10. Coils of wire Flux multiplies by the number of loops, therefore the induced voltage, induced current, and force will all be multiplied by N as well! If you completed the last treasure hunt, 2 bonus points will be added on to your test grade.

Don’t forget RHR #2! Thumb: Current Fingers: Field Palm: Push Also know how to use it with negative charges moving in B-fields!

Practice Problem #2 The square coil of wire shown has 20 turns, and is rotated by 90 degrees along the dotted line shown in an amount of time t. The wire has a resistance R, and is in an external magnetic field B. a)Write an expression for the average induced current in the loop. b)In which direction will the top and bottom of the wire feel a force? c)If the number of coils is doubled, what will happen to i)The resistance of the loop? ii)The emf? iii)The current through the loop?