Question

ough it.
a. Suppose that the radius of the loop were increasing. Use Lenz' law to explain why there would be an induced current through the wire. Indicate the direction of that current.

b. Check your answer regarding the direction of the induced current by considering the magnetic force that is exerted on the charge in the wire of the loop. "

"A copper wire loop is constructed so that its radius, r, can change. It is held near a solenoid that has a constant current through it.
a. Suppose that the radius of the loop were increasing. Use Lenz' law to explain why there would be an induced current through the wire. Indicate the direction of that current.

b. Check your answer regarding the direction of the induced current by considering the magnetic force that is exerted on the charge in the wire of the loop. "

Answer 1

Below are the answers:

a. There is a constant magnetic Feld, which means B is constant, so we can rewrite the change in fux as above.Because ΔA is positive, there will be a negative emf in the loop, corresponding to an induced magnetic momentpointing to the left on the page. The current in the loop will be into the page at the top and out of the page atthe bottom

V=-Δφ/ Δt = -B·ΔA/ Δt

b. As the loop’s radius is increasing, we can think about individual electrons in the wire loop as moving radiallyoutward. We’ll consider one in the top of the loop (which is moving up the page). Using the Lorentz ²orce Law

F=q(~v⇥~B)=qvB(ˆy⇥ˆx)=-qvBˆ

Constant forces pointing into the center of the loop will result in circular orbits (around the wire). Because theforce is pointing into the center of the loop, we know we have positive current at that point (into the page).