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# 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 different cases shown in Fig. 4.28?(image d )

4.24 (d) 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 different cases shown in Fig. 4.28? What is the force on each case? Which case corresponds to stable equilibrium?

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The magnetic field is

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

Current in the loop=12 A

Area of the loop = length$\times$breadth

A=0.1$\times$0.05

A=0.005 m2

$\vec{A}=0.005\ m^{2}(-\frac{\hat{i}}{2}+\frac{\sqrt{3}}{2}\hat{j})$

$\\\vec{\tau }=I\vec{A}\times \vec{B}\\ \\\vec{\tau }=12\times 0.005(-\frac{\hat{i}}{2}+\frac{\sqrt{3}}{2}\hat{j})\times 0.3\hat{k}\\ \\\vec{\tau }=-0.018(\frac{\hat{i}}{2}+\frac{\sqrt{3}}{2}\hat{j})$

The torque on the loop has a magnitude 0.018 Nm and at an angle of 240o from the positive-x direction. The force on the loop is zero.

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