Question

A charge q is accelerated through a potential difference V. It is then passed normally through a uniform magnetic field, where it moves in a circle of radius r. The potential difference required to move it in a circle of radius 2r is

• A. 2 V .
• B. 4 V
• C. 1 V
• D. 3 V

Answer 1

Answer: (B)

4 V

Answer 2

Radius of circular path: $r = \frac{\sqrt{2mqV}}{qB}$
$r \propto\sqrt{V}$ where B is constant
or $V \propto r^{2}$
$\frac{V_{2}}{V_{1}} = \left(\frac{r_{2}}{r_{1}}\right)^{2}$
$\frac{V_{2}}{V}= \left(\frac{2r}{r}\right)^{2} 4$
$\Rightarrow V_{2} = 4 V$