Question

A current loop of arbitrary shape lies in a uniform magnetic field B. Show that the net magnetic force acting on the loop is zero.

Answer 1

Given:
Uniform magnetic field existing in the region of the arbitrary loop = B
Let the electric current flowing through the loop be i.
Length of each side of the loop is l.
Assume that the direction of the current is clockwise.
Direction of the magnetic field is going into the plane of the loop.
Magnetic force is given by
`vecF = i veclxxvecB`
`vecF = ilBsintheta`

Here, θ = 90˚
Direction of force can be found using Fleming's lef- hand rule.
Force F₁ acting on AB = ilB upwards
Force F₂ acting on DC = ilB downwards
So, F₁ and F₂ cancel each other.
Force F₃ acting on AD = ilB outwards (Pointing towards the left from AB)
Force F₄ acting on BC = ilB outwards (Pointing towards the right from BC)
So, F₃ and F₄ cancel each other.
Therefore, the net force acting on the arbitrary loop is 0.