Question

Two charges -4q and q are kept at (-a, 0) and (a,0) respectively. The graph showing the variation of electric field
along x-axis is
​

Answer 1

Given info : Two charges -4q and +q are kept at (-a, 0) and (a, 0) respectively.

To choose : the graph showing the variation of the electric field along x - axis is..

solution : let A (-a, 0) and B(a, 0)

suppose a point P is placed between A and B such that AP = x so, BP = 2a - x

[ as distance between AB = a + a = 2a , so BP = AB - AP = 2a - x]

now, electric field due to -4q at P = k(4q)/x² (along PA)

electric field due to +q at P = kq/(2a - x)² (along PA)

so net electric field , E = 4kq/x² + kq/(2a - x)²

differentiating with respect to x we get,

dE/dx = -8kq/x³ + 2kq/(2a - x)³

at dE/dx = 0, x = 2a - x ⇒x = a

when -∞ < x < - a , dE/dx > 0 , increasing graph

when -a ≤ x ≤ 0 , dE/dx > 0 , increasing graph,

when 0 < x ≤ a, dE/dx < 0 , decreasing graph,

now you can just verify all options applying this conditions.

only option (3) is satisfying all the above condition.

Therefore the correct choice is (3)