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ABCD is a square loop having length of side ‘l’ and it is carrying a current i. The loop is placed in a region where a magnetic field $\vec{B} = - B_{o} (1 + \frac{x^{2}}{l^{2}}) \hat{k}$ exists as shown in figure. Then net force experienced by the loop is

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${ilB}_{0}$

${2ilB}_{0}$

${4ilB}_{0}$

${3ilB}_{0}$

answer is D.

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Detailed Solution

$|{\vec{F}}_{BC}| = |{\vec{F}}_{AD}|$

magnetic induction at the location of BC :

$B_{BC} = B_{o} [1 + {(\frac{2 l}{l})}^{2}] = 5 B_{o}$

magnetic induction at the location of AD

$B_{AD} = B_{o} [1 + {(\frac{l}{l})}^{2}] = 2 B_{o}$

$∴ F_{net} = i . l . 5 B_{o} - i . l . 2 B_{o} = 3 {ilB}_{o}$ .

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