Question

A long solenoid has 140 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 2.51 cm perpendicular to the solenoid axis. The speed of the electron is 0.0518c (c= speed of light, equal to 2.998 × 10⁸ m/s). Find the current i in the solenoid.

Answer 1

For this particular question-

we know that magnetic force = F = Q*V*B

And centripetal force = MV²/r

Now-

MV²/ r = Q*V*B

i.e

MV/r = Q*B ..(1)

9.11× 10^-31 * 0.0518*2.998*10⁸ / 2.51*10^-2 = 1.6*10^-19 * B

B = 0.35227 * 10^-2 T

Now we know that for solenoid-

B = $\mu _{0}$ * n*i

0.0035277 =  12.57 × 10⁻⁷ *140 *i

i = 20.017 Amp

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