A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that B is in plane of the coil. If due to a current i in the triangle a torque acts on it, the

Correct answer: C. 2( 3 B i )^ 1 / 2 Torque acting on equilateral triangle in a magnetic field B is =i A B θ Area of triangle LMN A= 3 4 l^2 and θ=90^ Substituting the given values in the expression for torque, we have aligned & =i × 3 4 l^2 B 90^ \& = 3 4 i l^2 B ( 90^ =1) aligned Hence, l=2( 3 B i )^ 1 / 2

JIPMER 2007

Exam: JIPMER
Year: 2007
Subject: Physics
Chapter: Magnetic Effects of Current

JIPMER 2007 · Physics · Magnetic Effects of Current

A coil in the shape of an equilateral triangle of side l is...

A coil in the shape of an equilateral triangle of side

l

is suspended between the pole pieces of a permanent magnet such that

\overrightarrow{\mathbf{B}}

is in plane of the coil. If due to a current

i

in the triangle a torque

\tau

acts on it, the side

l

of the triangle is A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet

Options

A $\frac{2}{\sqrt{3}}\left(\frac{\tau}{B i}\right)^{1 / 2}$
B $\frac{2}{\sqrt{3}}\left(\frac{\tau}{B i}\right)$
C $2\left(\frac{\tau}{\sqrt{3} B i}\right)^{1 / 2}$
D $\frac{1}{\sqrt{3}} \frac{\tau}{B i}$

Correct answer

C. $2\left(\frac{\tau}{\sqrt{3} B i}\right)^{1 / 2}$

Step-by-step solution

Torque acting on equilateral triangle in a magnetic field

\overrightarrow{\mathbf{B}}

\tau=i A B \sin \theta

Area of triangle LMN

A=\frac{\sqrt{3}}{4} l^2 and \theta=90^{\circ}

Substituting the given values in the expression for torque, we have

\begin{aligned}\tau & =i \times \frac{\sqrt{3}}{4} l^2 B \sin 90^{\circ} \& =\frac{\sqrt{3}}{4} i l^2 B\left(\because \sin 90^{\circ}=1\right)\end{aligned}

Hence, $l=2\left(\frac{\tau}{\sqrt{3} B i}\right)^{1 / 2}

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