A) \[\frac{E}{l}\]
B) \[\frac{2E}{2l}\]
C) \[\frac{2E}{3l}\]
D) \[\frac{E}{2l}\]
Correct Answer: B
Solution :
[b] Resistance of cylinder \[R=\int\limits_{0}^{\ell }{\frac{l}{\sigma }\frac{dx}{a}}=\frac{2\sqrt{\ell }}{3a{{\sigma }_{0}}}\] \[I=\frac{E}{R}\] Electric field \[=\frac{J}{\sigma }=\frac{I}{a.\sigma }=\frac{E\sqrt{x}}{Ra{{\sigma }_{0}}\ell }\] At \[x=\ell \] Electric field \[=\frac{E\left( \sqrt{\ell } \right)}{\frac{2\sqrt{\ell }}{3a{{\sigma }_{0}}}a{{\sigma }_{0}}\ell }=\frac{3E}{2\ell }\]
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