Question

An electron moves at a speed of 19000 m/s in a circular path of radius 2.2 cm in a solenoid. The magnetic field of the solenoid is perpendicular to the plane of the electron’s path. The permeability of free space is 4 π × 10−7 T · m/A. Find the strength of the magnetic field inside the solenoid. Answer in units of µT.

Find the current in the solenoid if it has 22 turns/cm. Answer in units of mA.

Answer 1

Given :-

v = 1.9 x 10^4 m/s

r = 2.2 cm = 2.2 x 10^-2 m

q = 1.6 x 10^-19 C

m = 9.11 x 10^-31 kg

a)

The magnetic force supplies to the centripetal acceleration,

qvB = mv^2 / r

B = mv / qr

B = (9.11 x 10^-31 x 1.9 x 10^4) / (1.6 x 10^-19 x 2.2 x 10^-2 m)

B = 4.92 x 10^-6 T

B = 4.92 uT

b)

n = 22 turns / cm

n = 2200 m^-1

uo = 4pi x 10^-7 T.m/A

The magnetic field inside the solenoid have magnitude of,

B = uonI

I = B/uon

I = (4.92 x 10^-6 T) / (4pi x 10^-7 x 2200)

I = 1.777 x 10^-3 A

I = 1.777 mA