Question

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

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

Answer 1

Answer: (B)

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