A solenoid has a length of 25 cm, a radius of 2 cm, 350 turns, and carries a 3 A

Question

A solenoid has a length of 25 cm, a radius of 2 cm, 350 turns, and carries a 3 A-current. The permeability of free space is 4pi times 10^-7 T middot m/A. Find the magnetic field on the axis at the center of the solenoid. Answer in units of mT. Find the flux through the solenoid, assuming B to be uniform. Answer in units of Wb. Find the self-inductance of the solenoid. Answer in units of mH. Find the magnitude of the induced emf in the solenoid when the current changes at 90 A/s. Answer in units of mV.

Explanation / Answer

(1)

B = uo ni

= uo ( N/L) i

= 4pi * 10^-7 ( 350/0.25) (3A)

=5.27* 10^-3 T

(2)

flux = BA = B pi r^2 = 5.27 * 10^-3 ( pi ( 0.02)^2 = 6.61 * 10^-6 Wb

(3)

L = uo N^2 A/l = 4 pi * 10^-7 ( 350)^2 ( pi ( 0.02)^2/0.25 = 0.779 mH

(4)

e= L di/dt = 0.779 * 10^-3 ( 90) = 70.11 mV

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