First slide

Force on a charged particle moving in a magnetic field

Question

The two particles X and Y, having equal charge, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii R₁ and R₂ respectively. The ratio of the mass of X to that of Y is

Easy

A

$\sqrt{(R_{1} / R_{2})}$
B

(R₁/R₂)²
C

(R₁/R₂)
D

(R₂/R₁)

Solution

$\frac{1}{2} {mv}^{2} = qV or v = \sqrt{(\frac{2 qV}{m})}$
In magnetic field $\frac{{mv}^{2}}{R} = qvB$
or $\frac{mv}{R} = qB or \frac{m}{R} \times \sqrt{\frac{2 qV}{m}} = qB$
or $\frac{\sqrt{m}}{R} = \frac{qB}{\sqrt{2 qV}} = \frac{\sqrt{q} \cdot B}{\sqrt{2 V}} = constant$
$∴ \frac{m_{X}}{M_{Y}} = {(\frac{R_{1}}{R_{2}})}^{2}$

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