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A charge of $+ 10 μ C$ and mass of 1gm is moving with velocity of 10⁶ m/s at an angle of 45° to x & y axis as shown. In this case it experiences a magnetic force along – ve z – direction. If it were projected with $10^{6} m / s$ along +ve z – direction, it would experience a magnetic force of $10^{- 2} N$ in +ve x-direction. The magnetic field $\vec{B}$ is:

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$- 10^{- 3} T (\hat{i} + \hat{j})$

$10^{- 3} T (\hat{j} + \hat{k})$

$10^{- 3} T \hat{i}$

$- 10^{- 3} T \hat{j}$

answer is D.

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Detailed Solution

$q = 10 μ C = 10^{- 5} C m = 10^{- 3} k g \vec{v} = 10^{6} [\frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j}]$

$\vec{F} = q [\bar{v} \times \bar{B}]$

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