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An infinite number of concentric rings c...

An infinite number of concentric rings carry a charge `Q` each alternately positive and negative. Their radii are `1, 2, 4, 8..` meters in geometric progression as shown in the figure. The potential at the centre of the rings will be

A

zero

B

`(Q)/(12pi epsilon_(0))`

C

`(Q)/(8pi epsilon_(0))`

D

`(Q)/(6pi epsilon_(0))`

Text Solution

Verified by Experts

The correct Answer is:
D
Potetnial at centre : `V = (kQ)/(1) - (kQ)/(2) + (kQ)/(4)`….
`kQ[1-(1)/(2)+(1)/(4)…] = (1)/(4pi epsilon_(0)) Q ((1)/(1+1//2)) = (Q)/(4pi epsilon_(0))`
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