Q. 15

# 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.

Let’s

assume a square magnetic loop

Let,
Uniform magnetic field existing in the region of the arbitrary loop = B
current flowing through the loop be i.

Length of each side of the loop be l.

Assuming the direction of the current clockwise.

Direction of the magnetic field is going towards the plane of the loop.

Magnetic force is given by where,

B= magnetic field

I = current

l = length of the wire

and θ = the angle between B and l  Here, θ = 900

Direction of force can be found using Fleming’s left-hand rule.

Force F1 acting on side AB is

= directed upwards

Force F2 acting on side DC = directed downwards

Since, F1 and F2 are equal and in opposite direction, they will cancel each other.

Similarly,

Force F3 acting on AD = directed outwards pointing

And

Force F4 acting on BC = directed outwards

Since, F3 and F4 are equal and in opposite direction, they will cancel each other

Hence, the net force acting on the arbitrary loop is 0.

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