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

Options

A. zero
B. ` ( Q) /( 12 pi epsi _ 0 ) `
C. ` (Q ) / (8 pi epsi _ 0 ) `
D. ` ( Q ) / ( 6pi epsi _ 0 ) `

Answer

D

Explanation

` V = (Q ) /( 4pi in _ 0 xx 1 ) - ( Q ) /( 4pi in _ 0 xx 2 ) + ( Q ) /( 4pi in _ 0 xx 2 ^ 2 )….oo `
` = ( Q ) /( 4 pi in _ 0 ) [ 1 - ( 1 ) /( 2 ) + ( 1 ) / ( 2 ^ 2 ) - ( 1 ) /( 2 ^ 3 ) + ….oo] `
` = ( Q ) / ( 4pi in _ 0 ) xx ( 1 ) /( 1 - (- 1//2 )) = ( Q ) /( 4pi in _ 0 ) xx ( 2 ) /( 3 ) = ( Q ) / ( 6 pi in _ 0 ) `