First slide

Magnetic force

Question

A charged particle carrying charge $1 μ C$ is moving with velocity $(2 \hat{i} + 3 \hat{j} + 4 \hat{k}) m s^{- 1}$ . If an external magnetic field of $(5 \hat{i} + 3 \hat{j} - 6 \hat{k}) \times 10^{- 3} T$ exists in the region where particle is moving , then the force on the particle is $\vec{F} \times 10^{- 9} N$ . The vector $\vec{F}$ is :

Easy

A

$- 300 \hat{i} + 320 \hat{j} - 90 \hat{k}$
B

$- 3.0 \hat{i} + 3.2 \hat{j} - 0.9 \hat{k}$
C

$- 0.30 \hat{i} + 0.32 \hat{j} - 0.09 \hat{k}$
D

$- 30 \hat{i} + 32 \hat{j} - 9 \hat{k}$

Solution

$\begin{array}{l} \vec{F} = q \vec{V} \times \vec{B} \\ \vec{F} \times 10^{- 9} = 10^{- 6} (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) \times (5 \hat{i} + 3 \hat{j} - 6 \hat{k}) \times 10^{- 3} \\ \vec{F} = |\begin{matrix} i & j & k \\ 2 & 3 & 4 \\ 5 & 3 & - 6 \end{matrix}| \times 10^{- 9} = (- 30 \hat{i} + 32 \hat{j} - 9 \hat{k}) \times 10^{- 9} \end{array}$

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