Two non-conducting sphere of radius R have charge Q uniformly distributed. The centres of sphere are `x = 0` and `x = 3R`. Find the magnitude and direction of the net electric field on the X-axis
(i) `x = 0`
(ii) `x = (R)/(2)`
(iii) `x = (3R)/(2)`
(iv) `x = 4R`

Explanation

O : origin `(x = 0)`
Electric field inside sphere at distance `r` from centre
`= (1)/(4 pi in_(0)) .(Qr)/(R^(3))`
On the surface or outside , whole change is assumed to be concentrated at centre.
(a) At `x = 0`,
`E_(1) = 0 , E_(2) = (1)/(4pi in_(0)) (Q)/((3R)^(2))` , towards left
`E_(n e t) = E_(2) = (Q)/(36 pi in_(0) R^(2))` , along `-x` axis
(b) At `x = R//2`,
`E_(1) = (1)/(4 pi in_(0)) .(QR//2)/(R^(3)) = (Q)/(8 pi in_(0) R^(2))` , along `+x`axis
`E_(2) = (1)/(4pi in_(0)) (Q)/((5R//2)^(2)) = (Q)/(25 pi in_(0) R^(2))` , along `-x`-axis
`E_(n e t) = E_(1) - E_(2) = (17 Q)/(200 pi in_(0) R^(2))`, along `+x` axis
(c ) At `x = 3R//2 , E_(n e t) = 0`
(d) At `x = 4R , E_(1) = (1)/(4 pi in_(0)) (Q)/((4 R)^(2)) , E_(2) = (1)/(4 pi in_(0)) (Q)/(R^(2))`
`E_(n e t) = E_(1) + E_(2) = (17 Q)/(64 pi in_(0) R^(2))` , along + x-axis