A charge +q is situated at a distance 'd' away from both the sides of a grounded conducting 'L' shaped sheet as shown in the figure.

The force acting on the charge +q is

Options

A. towards O, magnitude `(q^2)/(32piepsi_0d^2)(2sqrt2+1)`
B. away from O, magnitude `(q^2)/(32piepsi_0d^2)(2sqrt2+1)`
C. towards O, magnitude `(q^2)/(32piepsi_0d^2)(2sqrt2-1)`
D. away from O, magnitude `(q^2)/(32piepsi_0d^2)(2sqrt2-1)`

Answer

C

Explanation

By method of image, the given arrangement is equivalent to

`F_1=1/(4pivarepsilon_0(2d)^2),F_2=1/(4pivarepsilon_0)q^2/(2d)^2`
`F_3=1/(4pivarepsilon_0(2sqrt(2d))^2`
`therefore F_(nEt)=sqrt2q^2/(16pivarepsilon_0d^2)-q^2/(32pivarepsilon_0d^2)`
`q^2(32pivarepsilon_0d^2)2(sqrt2-1)` [towards O]