A) \[\frac{\lambda \omega {{R}^{3}}}{6}\]
B) \[\frac{\lambda \omega {{\ell }^{3}}}{3}\]
C) zero
D) \[\frac{\lambda {{\omega }^{2}}{{\ell }^{2}}}{3}\]
Correct Answer: C
Solution :
The charge on small element \[dq=\lambda \,dx\] Current, \[di=\frac{dq}{T}=\frac{(d\ell )\omega }{2\pi }\] Magnetic moment, \[\mu =\int_{{}}^{{}}{(di)A=\int\limits_{0}^{\ell }{\frac{\omega \cdot dq}{2\pi }\times \pi \,{{x}^{2}}}}\] \[=\frac{\omega \ell }{32}\left( \frac{{{\ell }^{3}}}{3} \right)=\frac{\omega \lambda {{\ell }^{3}}}{6}\] Similarly, same magnetic moment is there due to another rod in opposite direction, hence net becomes zero.You need to login to perform this action.
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