First slide

Force on a charged particle moving in a magnetic field

Question

The magnetic force acting on a charged particle of charge $- 2 μC$ in a magnetic field of 2 T acting in y direction, when the particle velocity is $(2 \hat{i} + 3 \hat{j}) \times 10^{6} {ms}^{- 1},$ is

Moderate

A

8 N in -z direction
B

4 N in z direction
C

8 N in y direction
D

8 N in z direction

Solution

When a charge q moves with velocity $\vec{v}$ inside magnetic field of strength $\vec{B}$ , then force on charge is called magnetic Lorentz force. The magnetic Lorentz force is in the direction of vector $\vec{V} \times \vec{B}$ .
Magnetic Lorentz force $\vec{F} = \vec{q} (\vec{V} \times \vec{B})$
$= - 2 \times 10^{- 6} [2 \times 2 \times 10^{6}]$ $\hat{k}$
= 8 N along negative z-axis

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