24.(b) 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?

Answers (1)
S Sayak

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\timesbreadth

A=0.1\times0.05

A=0.005 m2

\vec{A}=0.005\ m^{2}\hat{i} (same as that in the last case)

\\\vec{\tau }=I\vec{A}\times \vec{B}\\ \\\vec{\tau }=12\times 0.005\hat{i}\times 0.3\hat{k}\\ \\\vec{\tau }=-0.018\hat{j}

The torque on the loop has a magnitude of 0.018 Nm and acts along the negative-y-direction. The force on the loop is zero. This was exactly the case in 24. (a) as well.

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