Multiple - Choice Homework Problem 12.1 The circular solenoid drawn to the right

Question

Multiple - Choice Homework Problem 12.1 The circular solenoid drawn to the right has a radius R = 8cm. A square loop of wire with 1 turn and normal parallel to the axis of the solenoid is inside the solenoid. The length of one side of the square loop is l = 4cm. The solenoid is wound with N = 175 turns of over a length 25cm. The solenoid is connected to a resistor and therefore the current in the solenoid is decreasing according to the function where Io = 0.25A and r = 75s. The system is drawn to the right. The magnetic field in the solenoid points out of the page as drawn. Calculate the emf around the square loop (dark square) at t = 0.

Explanation / Answer

induced emf in square loop = e = NAdB/dt

A is area of the square

N = 1

magnetic field due to solonoid is B = uo n I

B = 4*3.14 e -7 * 175 * Io e^-t/T

so dB/dt = 0.0002198 * (-1/T) * Io e^(-t/T)

dB/dt = 0.0002198/75 * 0.25 * e^0

dB/dt = 0.732 uT/s

so emf e = 1 * 0.04* 0.04 * 0.732 e -6

emf e = 1.17 *10^-9 Volts

option A it is

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since EF and MF are perpendicular to each other

and here magnetic field is into the board

EF will in the form of circular motion around it

from RH rule this is Clockwise direction

so option D it is

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