Question 275: Magnetism and Matter

Question

The magnetic field existing in a region is given by $$\vec{B}=0.2(1+2 x) \hat{k}$$. A square loop of edge $$50 \mathrm{~cm}$$ carrying 0.5 A current is placed in $$x$$-$$y$$ plane with its edges parallel to the $$x$$-$$y$$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is _________ $$\mathrm{mN}$$.

Accepted Answer

$$\begin{aligned}
& \vec{F}_{B C}+\vec{F}_{D A}=0 \
& \vec{F}_{A B}=i l B=0.5 	imes 0.5(5)=1.25 \mathrm{~N} 	imes 0.2=0.25 \mathrm{~N} \
& \vec{F}_{C D}=0.5 	imes 0.5(6)=1.5 	imes 0.2=0.3 \mathrm{~N} \
& F_{	ext {net }}=0.05 \mathrm{~N} \
& \quad=50 \mathrm{mN}
\end{aligned}$$

Magnetism and Matter

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