Question

What is the radius of a tightly wound solenoid of circular cross-section that has 180 turns if a change in its internal magnetic field of 3.0 T/s causes a 6.0 A current to flow? The resistance of the circuit that contains the solenoid is 17 Ω. The only emf source for the circuit is the induced emf. A. 0.54 m B. 0.043 m C. 0.25 m D. 0.014 m

Answer 1

C. 0.25 m

Step-by-step explanation:

Given;

current flow in the solenoid, I = 6.0 A

number of turns of the solenoid, N = 180 turns

the resistance of the circuit, R = 17 Ω

change in the magnetic field, dB/dt = 3.0 T/s

The emf of the circuit is given by;

V = IR

V = 6 x 17

V = 102 Volts

Magnitude of induced emf is given by;

`E = N((dB)/(dt) )A`

Where;

A is area of the solenoid

`E = N((dB)/(dt) )A\\\\A = (E)/(N((dB)/(dt) )) \\\\A = (102)/(180 *3) \\\\A = 0.18889 \ m^2`

Area of the circular solenoid is given by;

A = πr²

where;

r is radius of the solenoid

`r = \sqrt{(A)/(\pi) }\\\\r = \sqrt{(0.18889)/(\pi) }\\\\r = 0.25 \ m`

Therefore, the correct option is C. 0.25 m