A charge 2.0μC  moves with a speed of 2.0×106ms−1  along the positive x- axis. A magnetic field  B→ of strength 0.20j^+0.40k^T  exists in space. Find the magnetic force acting on the charge.

# A charge $2.0\mathrm{\mu C}$  moves with a speed of $2.0×{10}^{6}{\mathrm{ms}}^{-1}$  along the positive x- axis. A magnetic field  $\stackrel{\to }{\mathrm{B}}$ of strength $\left(0.20\stackrel{^}{\mathrm{j}}+0.40\stackrel{^}{\mathrm{k}}\right)\mathrm{T}$  exists in space. Find the magnetic force acting on the charge.

1. A

$\left(0.8\stackrel{^}{\mathrm{k}}-1.6\stackrel{^}{\mathrm{j}}\right)\mathrm{N}$

2. B

$\left(0.5\stackrel{^}{\mathrm{k}}-1.6\stackrel{^}{\mathrm{j}}\right)\mathrm{N}$

3. C

$\left(0.5\stackrel{^}{\mathrm{k}}-2.6\stackrel{^}{\mathrm{j}}\right)\mathrm{N}$

4. D

$\left(0.5\stackrel{^}{\mathrm{j}}-2.1\stackrel{^}{\mathrm{k}}\right)\mathrm{N}$

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### Solution:

The force on the charge $=\mathrm{q}\stackrel{\to }{\mathrm{v}}×\stackrel{\to }{\mathrm{B}}$
$\begin{array}{l}=\left(2.0×{10}^{-6}\mathrm{C}\right)\left(2.0×{10}^{6}{\mathrm{ms}}^{-1}\stackrel{^}{\mathrm{i}}\right)×\left(0.20\stackrel{^}{\mathrm{j}}+0.40\stackrel{^}{\mathrm{k}}\right)\mathrm{T}\\ =4.0\left(0.20\stackrel{^}{\mathrm{i}}×\stackrel{^}{\mathrm{j}}+0.40\stackrel{^}{\mathrm{i}}×\stackrel{^}{\mathrm{k}}\right)\mathrm{N}\\ =\left(0.8\stackrel{^}{\mathrm{k}}-1.6\stackrel{^}{\mathrm{j}}\right)\mathrm{N}\end{array}$  Register to Get Free Mock Test and Study Material

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