A current of 2 A enters at the corner *d* of a square frame *abcd* of side 20 cm and leaves at the opposite corner *b*. A magnetic field *B* = 0.1 T exists in the space in a direction perpendicular to the plane of the frame, as shown in the figure. Find the magnitude and direction of the magnetic forces on the four sides of the frame.

#### Solution

Given:

A square frame abcd of side, *l *= 20 cm

Electric current through the wire, *I* = 2 A

Magnetic field, *B* = 0.1 T

The direction of magnetic field is perpendicular to the plane of the frame, coming out of the plane.

As per the question, current enters at the corner *d* of the square frame and leaves at the opposite corner *b.*

Angle between the frame and magnetic field, *θ *= 90˚

Magnetic force,

`vecF = i vecl xx vecB`

For wire *da *and *cb*,

`|vecF| = ilBsin theta`

`|vecF| = ilBsin90°`

`= 2/2 xx 20 xx 10^-2xx 0.1`

= 0.02 N

The direction of force can be found using Fleming's left-hand rule.

Thus, the direction of magnetic force is towards the left.

For wires *dc *and *ab*,

`|vecF| = ilBsintheta`

∴ `|vecF| = ilBsin90^circ`

`= 2/2 xx 20 xx 10^-2xx0.1`

`= 0.02 N`

The direction of force can be found using Fleming's left-hand rule.

Thus, the direction of magnetic force is downwards.