In an electric field, the potential V(x), depending only on the x-coordinate, is given by `V(x) = ax -bx^(3)`, where a and b are constants, find out the points on the x -axis where the electric field intensity would vanish.

Explanation

`E = -(dV)/(dx) = -d/(dx) (ax-bx^(3)) = -a + 3bx^(2)`
E would vanish, i.e., E = 0, under this condition that,
`-a + 3bx^(2) = 0 or, x^(2) = a/(3b) or, x = +- sqrt((a)/(3b))`
`:.` The electric field intensity vanishes at the points
`x = sqrt((a)/(3x)) and x = -sqrt((a)/(3b))`, on the x-axis.