A ten-turn circular wire loop with a radius of 1 cm and resistance 0.0200 is hel

Question

A ten-turn circular wire loop with a radius of 1 cm and resistance 0.0200 is held stationary above a vertically aligned solenoid as shown in the diagram. The solenoid is attached to a power supply similar to the ones in lab, and the sense in which the current flows through the solenoid is clockwise as viewed from above.
The solenoid creates a nearly homogeneous magnetic field near the wire loop with magnitude B = 0.0060 T at t = 0 s.

Between times t = 2 s and t = 4 s, the current of the power supply is steadily increased (i.e., the rate at which the current through the solenoid increases is constant) until the current through the solenoid is doubled as shown in the graph below.

Part H

What is the magnitude of the magnetic flux through the wire loop at t = 1 s?

Part I

What is magnitude of the rate-of change of the magnetic flux through the wire loop at t = 3 s?

Part J

What is the magnitude of the EMF in the wire loop at t = 3 s?

unit= V

Explanation / Answer

N = 10 turns,

r = 1.0 cm.

R = 0.02 ohm.

at t = 0 s, B = 0.006 T.

The current through the solenoid doubles between t = 2 s and t = 4 s

.so B doubles in 2 s interval, dB/dt = 0.006/2 = 0.003T/s

A)
flux F = N*B*pi*r^2 = 10*0.006*3.14*(0.01)^2 = 18.84*10^(-6) Wb

B)
dF/dt = N*pi*r^2*dB/dt = 10*3.14*(0.01)^2 * 0.003 = 9.42*10^(-6) Wb/s

C)
the magnitude of the EMF = dF/dt = 9.42*10^(-6) V

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