A charged particle of change 4mc enters a uniform magnetic field of induction $\bar{B} = 4 \hat{i} + y \hat{j} + z \hat{k}$ tesla with a velocity $\bar{v} = 2 \hat{i} + 3 \hat{j} - 6 \hat{k}$ . If the particle continues to move un deviated, then the strength of the magnetic field induction (B) is ____ tesla

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Detailed Solution

F = 0 \Rightarrow \vec{V} \times \vec{B} = 0

$\Rightarrow \frac{2}{4} = \frac{3}{y} = \frac{- 6}{z}$

$\Rightarrow y = 6 and z = - 12$

$\vec{B} = 4 \hat{i} + 6 \hat{j} - 12 \hat{k}$

$B = \sqrt{4^{2} + 6^{2} + {(- 12)}^{2}}$

$= \sqrt{16 + 36 + 144}$

$= \sqrt{196} = 14 T$

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