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Question 6.1: Calculate the torque exerted on the square loop shown in Fig...

Calculate the torque exerted on the square loop shown in Fig. 6.6, due to the circular loop (assume r is much larger than a or b). If the square loop is free to rotate, what will its equilibrium orientation be?

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N = m _{2} \times B _{1} ; B _{1}=\frac{\mu_{0}}{4 \pi} \frac{1}{r^{3}}\left[3\left( m _{1} \cdot \hat{ r }\right) \hat{ r }- m _{1}\right] ; \hat{ r }=\hat{ y } ; m _{1}=m_{1} \hat{ z } ; m _{2}=m_{2} \hat{ y } . \quad B _{1}=-\frac{\mu_{0}}{4 \pi} \frac{m_{1}}{r^{3}} \hat{ z }.

N =-\frac{\mu_{0}}{4 \pi} \frac{m_{1} m_{2}}{r^{3}}(\hat{ y } \times \hat{ z })=-\frac{\mu_{0}}{4 \pi} \frac{m_{1} m_{2}}{r^{3}} \hat{ x } . \text { Here } m_{1}=\pi a^{2} I, m_{2}=b^{2} I . \text { So } N =-\frac{\mu_{0}}{4} \frac{(a b I)^{2}}{r^{3}} \hat{ x } .

Final orientation : downward (-\hat{ z }) .

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