Question

A long solenoid has 150 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 2.68 cm perpendicular to the solenoid axis. The speed of the electron is 0.0404c (c = speed of light, equal to 2.998 x 108 m/s). Find the current i in the solenoid. Number Units the tolerance is +/-2%

Answer 1

Given,

Number of turns, N = 150 turns/cm = 150 * 100 turns / m

The radius of the circle, r = 2.68 cm = 0.0268 m

The speed of the electron, v = 0.0404 c ; where c = 2.998 * 10⁸ m/s

= 0.0404 * 2.998 * 10⁸

We know,

mv² / r = q v B

B = mv / q r

Where,

m is the mass of an electron = 9.1 * 10^-31 Kg

q is the charge = 1.6 * 10^-19 C

B = ( 9.1 * 10^-31 * 0.0404 * 2.998 * 10⁸ ) / (1.6 * 10^-19 * 0.0268)

= 2.57 * 10^-3 T

The current in a solenoid is,

From B = $\mu$ ₀ n I

So, I = B / $\mu$ ₀ n

= (2.57 * 10^-3) / (4$\pi$ * 10^-7 * 150 * 100)

= 0.1364 A