Question

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.
Figure

Answer 1

Explanation:

To find : The magnitude and direction of the magnetic forces on the four sides of the frame.

abcd side of a square frame, l = 20 cm

Magnetic field, B = 0.1 T

Electric current passing in the wire, I = 2 A

The magnetic field’s direction is perpendicular to the frame plane, impending out of the plane.

As per the provided information, at the corner d, the current enters the square frame and at the opposite corner b, it leaves.

Angle between the frame and magnetic field,$\theta=90^{\circ}$

Magnetic force, $\vec{F}=i \vec{l} \times \vec{B}$

For wire da and cb,

$\begin{aligned}&|\vec{F}|=i l B \sin \theta\\&\therefore|\vec{F}|=i l B \sin 90^{\circ}\end{aligned}$

$\begin{aligned}&=\frac{2}{2} \times 20 \times 10^{-2} \times 0.1\\&=0.02 \mathrm{N}\end{aligned}$

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,

$\begin{aligned}&|\vec{F}|=i l B \sin \theta\\&\therefore|\vec{F}|=i l B \sin 90^{\circ}\end{aligned}$

$\begin{aligned}&=\frac{2}{2} \times 20 \times 10^{-2} \times 0.1\\&=0.02 N\end{aligned}$

The direction of force can be found using Fleming's left-hand rule. Thus, the direction of magnetic force is downwards.