A small current-carrying coil having a megantic moment `p_(m)` is located at the axis of a round loop of radius `R` with current `I` flowing thorough it. Find the magnitude of the vector force applied to the coil if its distance from the centre of the loop is equal to `x` and the vector `p_(m)` coincides in direction with the axis of the loop.

Explanation

`F_(x) = p_(m) (del)/(del x) B_(x)`
But, `B_(x) = (mu_(0) I)/(4pi) int (Rdl)/((x^(2) + R^(2))^(3//2)) (3)/(2) = (mu_(0) IR^(2))/(2(x^(2) + R^(2))^(3//2))`
So `F = (mu_(0))/(4pi) (I.2pi R^(2))/((x^(2) + R^(2))^(5//2)) (3)/(2) . 2x p_(m)`
`= (mu_(0) 6pi R^(2) I p_(m) x)/(4pi (x^(2) + R^(2))^(5//2))`