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A very large non-conducting plane carryi...

A very large non-conducting plane carrying charge `Q` uniformly distributed over it is placed in a medium with resistively `rho` and permittivity `epsilon`. The plane leaks charge through the surrounding medium and the charge becomes `1/n` times the initial value after a time `t=6rho epsilon ln(2)` elapses. Find the integer value `n`. (Neglect the end effects).

Text Solution

Verified by Experts

The correct Answer is:
8
`J-1/(rho) E=(sigma)/(2rho epsilon)`
`I=jA=q/(2rho epsilon)implies(dq)/(dt)=-q/(2rho epsilon)` ltbRgt `impliesq=Qd^(-(t/(2rho epsilon)))`
or `q=Q/8` at `t=5 rho epsilon ln(2)`
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