Question:
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 the plane of the coil. If due to current i in the triangle, a torque τ 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 such that B is in the plane of the coil. If due to current i in the triangle, a torque τ acts on it. The side l of the triangle is
Updated On: Jun 26, 2024
$2(\frac{τ}{\sqrt3Bi})^{\frac{1}{2}}$
$\frac{2}{\sqrt3}(\frac{τ}{Bi})$
$\frac{1}{\sqrt3}(\frac{τ}{Bi})$
$\frac{2}{\sqrt3}(\frac{τ}{Bi})^{\frac{1}{2}}$
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The Correct Option is A
Solution and Explanation
The Correct option is A: $2(\frac{τ}{\sqrt3Bi})^{\frac{1}{2}}$
The current flowing clockwise in the equilateral triangle has a magnetic field in the direction of $\hat{k}$
τ = $BiNAsinθ$
τ = $BiNAsin90^o$
Area of equilateral triangle: $\frac{\sqrt{3}}4 I^2$
τ = $Bi×\frac{\sqrt{3}}4 I^2$
$\therefore I^2 = \frac{4τ}{\sqrt{3} Bi}$ = $2(\frac{τ}{\sqrt3Bi})^{\frac{1}{2}}$
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