First slide

Torque on a current carrying loop placed in uniform magnetic field

Question

The loop ABCDEFGH, shown in figure, is carries a current i. A uniform magnetic field $\vec{B}$ exists in that region of space as shown in figure. Then magnetic torque experienced by the loop is,
[Given, AB = BC = CD =l and EF = FG = GH = l/2]

Moderate

A

$\frac{1}{4} i l^{2} B$
B

$\frac{1}{2} i l^{2} B$
C

$\frac{3 i l^{2} B}{4}$
D

$\frac{3}{8} i l^{2} B$

Solution

Magnetic dipole moment, of the loop, $M = [l^{2} - {(\frac{l}{2})}^{2}] i = \frac{3 l^{2} i}{4}$ and it is inward.
$∴ τ = MBsin 90^{o} = \frac{3 i l^{2} B}{4}$

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