A non conducting ring (of mass m, radius \[r\], Having charge\[Q\]) is placed on a rough horizontal Surface (in a cylindrical region with transverse magnetic field). The field is increasing with time at the rate \[R\] and coefficient of friction between The surface and the ring is \[\mu \]. For ring to remain in equilibrium u should be greater than equal to, |
A) \[\frac{Q{{r}^{2}}{{R}^{2}}}{2mg}\]
B) \[\frac{QrR}{2mg}\]
C) \[\frac{Q{{r}^{2}}R}{2mg}\]
D) \[\frac{Qr{{R}^{2}}}{2mg}\]
Correct Answer: B
Solution :
Induced electric field |
\[E=\frac{r}{2}\left( \frac{dB}{dt} \right);=\frac{rR}{dt}\] |
This electric field exerts tangentive force on each part of the ring. So net force, |
\[F=EQ=\frac{rRQ}{2}\] |
For ring to be in equilibrium, |
\[F\le {{F}_{friction}}\] |
\[\operatorname{or}\,r\frac{RQ}{2}\le \mu mg\] |
\[\therefore \,\,\,\,\mu \ge \frac{rRQ}{2mg}\] |
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