Question

A charge (q, m) perpendicularly enters a semi - infinite B - field with a speed v. Find the deviation and the time it spends in the B-field.

• A. $\frac{\pi }{2},\frac{\pi m}{2qB}$
• B. $\pi ,\frac{\pi m}{qB}$
• C. $2\pi ,\frac{2\pi m}{qB}$
• D. $\frac{\pi }{4},\frac{\pi m}{qB}$

Answer 1

The correct option is B $\pi ,\frac{\pi m}{qB}$

The charged particle follows a circular path after entering the magnetic field and since the field is semi infinite, the charge completes half rotation and leaves the magnetic field perpendicularly.
So,
Deviation = $\pi$ radians

Also, r = $\frac{mv}{qB}$
Time spent in the magnetic field is $\frac{\pi r}{v}$

$\Rightarrow \frac{\pi m}{qB}$