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Q.

A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially present in a perpendicular magnetic field $\vec{B} = B_{o} (- \hat{k})$ as shown in figure. If current in the wire is ‘i’ then the magnetic force on the wire is

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a

$- 2 iBR \hat{j}$

b

$2 iBR \hat{j}$

c

$- iBR \hat{j}$

d

$iBR \hat{j}$

answer is B.

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Detailed Solution

$\begin{array}{l} F = i (\vec{l} \times \vec{B}) \\ = i [2 R \hat{i} \times B (- \hat{k})] \\ = 2 iBR (\hat{j}) \end{array}$

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