A charged particle carrying charge 1μC is moving with velocity 2i^+3j^+4k^ms−1. If an external magnetic field of 5i^+3j^−6k^×10−3T exists in the region where particle is moving , then the force on the particle is F→×10−9N . The vector F→ is :

F→=qV→×B→F→×10−9=10−62i^+3j^+4k^×5i^+3j^−6k^×10−3F→=ijk23453−6×10−9=−30i^+32j^−9k^×10−9

A charged particle carrying charge 1μC is moving with velocity 2i^+3j^+4k^ms−1. If an external magnetic field of 5i^+3j^−6k^×10−3T exists in the region where particle is moving , then the force on the particle is F→×10−9N . The vector F→ is :

F→=qV→×B→F→×10−9=10−62i^+3j^+4k^×5i^+3j^−6k^×10−3F→=ijk23453−6×10−9=−30i^+32j^−9k^×10−9

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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 :

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

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

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

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

answer is D.

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Detailed Solution

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