Two identical conducting spheres of radius r separated far apart are joined through resistor R & a switch S . Initially switch is open and one of the spheres is provided with a charge + Q 0 . Switch

Question

Two identical conducting spheres of radius r separated far apart are joined through resistor R & a switch S . Initially switch is open and one of the spheres is provided with a charge + Q 0 ​ . Switch S is closed at t = 0 . If charge on sphere B at time t = 26 k 65 rR ​ is given by Q = a [ 1 − e − n ] (where a & n are constant), find the value of n.

TestHub · Accepted Answer

Charge flow equalises the two sphere potentials: $\frac{d q}{d t} = \frac{k}{R r} (Q_{0} - 2 q)$ , which solves to $Q = \frac{Q _{0}}{2} (1 - e^{- 2 k t / r R})$ .

At $t = \frac{65 r R}{26 k}$ the exponent is $\frac{2 k}{r R} \cdot \frac{65 r R}{26 k} = 5$ , so n = 5.

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