Question

A particle with charge q and mass m is projected with kinetic energy K into the region between two plates of a uniform magnetic field B as shown below.

If the particle is to miss collision with the opposite plate, the maximum value of B is

• A. $\frac{\sqrt{2K}}{qmd}$
• B. $\frac{\sqrt{2Kd}}{qm}$
• C. $\frac{\sqrt{2Km}}{qd}$
• D. $\frac{\sqrt{2Kq}}{md}$

Answer 1

The correct option is C $\frac{\sqrt{2Km}}{qd}$

Given that, $\frac{1}{2}m{v}^2=K$
$\Rightarrow v=\sqrt{\frac{2K}{m}}$
To just miss collision with the opposite plate, the particle must move in a radius r which is equal to d.
Now, $r=\frac{mv}{qB}\Rightarrow d=\frac{m\sqrt{\frac{2K}{m}}}{qB}$
Solving we get, $B=\frac{\sqrt{2Km}}{qd}$