A) \[\frac{\rho I}{2\pi a}-\frac{\rho I}{2\pi \left( a+b \right)}\]
B) \[\frac{\rho I}{2\pi \left( a-b \right)}\]
C) \[\frac{\rho I}{\pi a}-\frac{\rho I}{\pi \left( a+b \right)}\]
D) \[\frac{\rho I}{a}-\frac{\rho I}{\left( a+b \right)}\]
Correct Answer: C
Solution :
\[E=\rho \,j=\rho \frac{I}{2\pi {{r}^{2}}}\] Potential difference due to current at A \[{{V}_{B}}-{{V}_{C}}=-\int\limits_{C}^{B}{\vec{E}.\,\,d\vec{l}=-\int\limits_{a+b}^{a}{\rho \frac{I}{2\pi {{r}^{2}}}.\,dr\,;}}\]\[\Delta V'=-\frac{\rho I}{2\pi }\left[ -\frac{1}{r} \right]_{a+b}^{a}=\frac{\rho I}{2\pi a}-\frac{\rho I}{2\pi \left( a+b \right)}\] By principle of superposition, \[\Delta V=2\Delta V'=\frac{\rho I}{\pi a}-\frac{\rho I}{\pi \left( a+b \right)}\]You need to login to perform this action.
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