A wire carrying a current along the positive -axis has length . It is kept in a magnetic field . The magnitude of the magnetic force acting on the wire is [2023]

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Solution

Q.
A wire carrying a current $I$ along the positive $x$ -axis has length $L$ . It is kept in a magnetic field $\vec{B} = (2 \hat{i} + 3 \hat{j} - 4 \hat{k})$ $T$ . The magnitude of the magnetic force acting on the wire is [2023]

1 $5 I L$

2 $\sqrt{3} I L$

3 $3 I L$

4 $\sqrt{5} I L$

Ans.
(1)

Given $\vec{B} = (2 \hat{i} + 3 \hat{j} - 4 \hat{k})$ $T$

$\vec{F} = I \vec{L} \times \vec{B} = I L \hat{i} \times (2 \hat{i} + 3 \hat{j} - 4 \hat{k})$ $;$ $\vec{F} = 3 I L \hat{k} + 4 I L \hat{j}; F = 5 I L$

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