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4.24(e) A uniform magnetic field of 3000 G is established along the positive z-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. What is the torque on the loop in the given case shown in Figure (e)? What is the force in this case? 

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The magnetic field is given as,

$$
\vec{B}=3000 G \hat{k}=0.3 T \hat{k}
$$


Current in the loop $=12 \mathrm{Amp}$
Area of the loop $=$ length $\times$ breadth
The area under the loop $(A)=0.1 \times 0.05=0.005 \mathrm{~m}^2$
Torque $\tau=I \vec{A} \times \vec{B}$

$$
\begin{aligned}
& =\left(50 \times 10^{-4} \times 12\right) \hat{k} \times 0.3 \hat{k} \\
& =0
\end{aligned}
$$
 

Hence, the torque is zero. The force is also zero. In this case, the direction of the current in both directions is the same and the angle between them is zero.

If displaced, they come back to an equilibrium. Hence, its equilibrium is stable.

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Sayak

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