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Faraday's Law

The magnetic ...

Question

The magnetic field in a region given by $\to B = B_{0} (1 + \frac{2 x}{l})^k$ . A square loop of edge $l$ carrying a current $i$ , is placed with one of 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

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B

zero

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C

i B_{0} l

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D

2 i B_{0} l

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Solution

The correct option is D $2 i B_{0} l$
Given,

$B = B_{0} (1 + \frac{2 x}{l})^k$

At $x = 0, B_{1} = B_{0}^k$

At $x = l, B_{2} = 3 B_{0}^k$

Net force,

$F_{n e t} = F_{2} - F_{1} = i l (B_{2} - B_{1})$

$= i l (3 B_{0} - B_{0})$

$= 2 i l B_{0}$

Hence, option (d) is the correct answer.

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