An infinite number of charges each q are placed in the x-axis at distances of 1, 2, 4, 8, ………meter from the origin. If the charges are alternately positive and negative find the intensity of electric field at origin.

Explanation

The electric field
`E = (Q)/( 4 pi in_(0)) (1- (1)/(2^(2)) +(1)/(4^(2)) -(1)/(8^(2)) + ……) `
`= (Q)/( 4 pi in_(0)) (1)/([ 1 - ((-1)/(4))]) =(Q)/( 4pi in_(0)) . (4)/(5)`
since the expression in the bracket is in GP with a common ratio `=(1)/(2^(2)) = (1)/(4)`.
`E =(4)/(5) . (Q)/( 4pi in_(0)) `
`E = (Q)/( 5 pi in_(0))`