First slide

Force on a charged particle moving in a magnetic field

Question

A particle of specific charge $\frac{q}{m} = π C / kg$ is projected from the origin towards positive x-axis with a velocity of 10 m/s in a uniform magnetic field $\vec{B} = - 2 \hat{k} T .$ The velocity v of particle after time $t = \frac{1}{12} s$ will be (in m/s)

Moderate

A

$5 [\hat{i} + \sqrt{3} \hat{j}]$
B

$5 (\sqrt{3} \hat{i} + \hat{j})$
C

$5 [\sqrt{3} \hat{i} - \hat{j}]$
D

$5 [\hat{i} + \hat{j}]$

Solution

The particle will move in xy plane in circular path with angular velocity
$ω = α B = 2 π r a d / s . T h e r e f o r e a n g l e o f r o t a t i o n = 2 π \times \frac{1}{12} r a d = 30^{0}$
$\begin{array}{l} \vec{v} = 10 [\cos 30 \hat{i} + \sin 30 \hat{j}] \\ \vec{v} = 10 [\frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j}] = 5 [\sqrt{3} \hat{i} + \hat{j}] m / s \end{array}$

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