Question

A particle with a specific charge $s$ is fired with a speed $v$ towards a wall at a distance $d$, perpendicular to the wall. What minimum magnetic field must exist in this region for the particle not to hit the wall?

• A. $\frac{v}{sd}$
• B. $\frac{2v}{sd}$
• C. $\frac{v}{2sd}$
• D. $\frac{v}{4sd}$

Answer 1

The correct option is A $\frac{v}{sd}$

The particle moves in a circle of radius $d$ if it will just miss the wall.

$\frac{m{v}^2}{r}=qvB$

$\therefore mv=qBr$

$\therefore B=\frac{v}{\frac{q}{m}r}=\frac{v}{sd}$