Question

A wire of arbitrary shape carries a current $I=2A$ . Consider the portion of wire between $\left(\right.0,0,0\left.\right)$ and $\left(\right.4,4,4\left.\right).$ A magnetic filled given by $\overset{ \rightarrow }{B}=\left(12 \times \left(10\right)^{- 4} \hat{i} + 2 \times \left(10\right)^{- 4} \hat{j}\right)$ $T$ exists in the region. The force acting on the given portion the wire is

• A. $\overset{ \rightarrow }{F}=\left[\left(\hat{i} + \hat{j} + \hat{k}\right) \times \left(12 \hat{i} + 12 \hat{j}\right)\right]N$
• B. $\overset{ \rightarrow }{F}=8\times \left(10\right)^{- 4}\left[\left(\hat{i} + \hat{j} + \hat{k}\right) \times \left(12 \hat{i} + 2 \hat{j}\right)\right] \, N$
• C. Zero
• D. None of the above

Answer 1

Answer: (B)

The magnetic force in the uniform magnetic field is
$\overset{ \rightarrow }{F}=I\left(\right.\overset{ \rightarrow }{L}\times \overset{ \rightarrow }{B}\left.\right)$
$\overset{ \rightarrow }{L}=4\hat{i}+4\hat{j}+4\hat{k}$ and
$\overset{ \rightarrow }{B}=\left(\right.12\hat{i}+2\hat{j}\left.\right)\times \left(10\right)^{- 4}T$
$\therefore \overset{ \rightarrow }{F}=8\times \left(10\right)^{- 4}\left[\right.\left(\right.\hat{i}+\hat{j}+\hat{k}\left.\right)\times \left(\right.12\hat{i}+2\hat{j}\left.\right)\left]\right.N$