Question

The magnetic field existing in a region is given by $\vec{B}=B_{0}\left(1+\frac{x}{1}\right) \hat{k}$. A square loop of edge $l$ and carrying a current $i$, is placed with its edge parallel to the $x-y$ axes. Find the magnitude of the net magnetic force experienced by the loop

• A. $\frac{1}{2} i B_{0} l$
• B. Zero
• C. $i B_{0} l$
• D. $2 i B_{0} l$

Answer 1

Answer: (C)

$\vec{B}=B_{0}\left(1+\frac{x}{l}\right) \hat{k}$
at $x=0, B_{1}=B_{0} \hat{k}$
at $x=I, B_{2}=2 B_{0} \hat{k}$
$F_{\text {net }} =F_{2}-F_{1}=i l\left(B_{2}-B_{1}\right) $
$=i l\left(2 B_{0}-B_{0}\right) $
$=i l B_{0}$