A) \[\frac{3\,R\,{{\tau }^{3}}}{{{a}^{2}}}\]
B) \[\frac{{{a}^{3}}}{3\,R{{\tau }^{2}}}\]
C) \[\frac{3R\,a\tau }{4}\]
D) \[\frac{{{a}^{2}}{{\tau }^{2}}}{3R}\]
Correct Answer: D
Solution :
The net amount of heat generated in a small time dt is \[dQ=\frac{{{E}^{2}}}{R}dt\] \[E=\,\,-\,\frac{d\phi }{dt}=(2at\,-\,a\tau )\] \[\Rightarrow \,\,\,\,\,\,dQ=\frac{{{(2at-a\tau )}^{2}}}{R}dt\] \[Q=\int\limits_{0}^{\tau }{\frac{{{(2at-a\tau )}^{2}}}{R}}dt=\frac{{{a}^{2}}{{\tau }^{3}}}{3\,R}\]
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