Directions: are based on the following paragraph |
Consider a block of conducting material of resistivity \[\rho \] shown in the figure. Current I enters at A and leaves from D. |
We apply superposition principal to find voltage \[\Delta V\] developed between B and C. The calculation is done in the following steps: |
(i) Take current I entering from A and assume it to spread over a hemispherical surface in the block. |
(ii) Calculate field E(r) at distance r from A by |
using Ohms law \[E=\rho j\], where j is the current per unit area at r. |
(iii) From the r dependence of E(r), obtain the potential V(r) at r. |
(iv) Repeat (i), (ii) and (iii) for current I leaving D and superpose results for A and D. |
For current entering at A, the electric field at a distance r from A is [AIEEE 2008] |
A) \[\frac{\rho I}{2\pi {{r}^{2}}}\]
B) \[\frac{\rho I}{4\pi {{r}^{2}}}\]
C) \[\frac{\rho I}{8\pi {{r}^{2}}}\]
D) \[\frac{\rho I}{{{r}^{2}}}\]
Correct Answer: A
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