Question

A proton and helium nucleus are shot into a magnetic field at right angles to the field with same kinetic energy. Then the ratio of their radii is

• A. 1:01
• B. 1:02
• C. 2:01
• D. 1:04

Answer 1

Answer: (A)

1:01

Answer 2

The radius of the circular path, of a charges particle in magnetic field
$r=\frac{m v}{q B}=\sqrt{\frac{2 m E}{q B}}$
Here, kinetic energy for proton and helium is same and both are moving in the same magnetic field
$\therefore r \propto \frac{\sqrt{m}}{q}$
So, $\frac{r_{p}}{r_{ e }}=\frac{\frac{\sqrt{m_{p}}}{q_{p}}}{\frac{\sqrt{m_{ He }}}{q_{ He }}}=\sqrt{\frac{m_{p}}{m_{ He }}} \times \frac{q_{ He }}{q_{p}}=\sqrt{\frac{m}{4 m}} \cdot \frac{2 q}{q}=\frac{1}{1}$