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 τ acts on it, the side l of the triangle is (a) 2/√(3)((τ)/(Bi)) (b) 2((τ)/(√(3)Bi))1/2 (c) 2/√(3)((τ)/(Bi))1/2 (d) 1/√(3)(τ)/(Bi)

Answer: (b). B in the plane of the coil, so m ⊥ B: τ = iAB. Area of equilateral triangle A = √(3)/4l² ⇒ τ = √(3)/4l² iB l² = (4τ)/(√(3)Bi) ⇒ l = 2((τ)/(√(3)Bi))1/2 So the answer is (b).

A coil in the shape of an equilateral triangle of side l is suspended… | NEET 2005 (AIPMT)

Q30NEET 2005 · AIPMTDifficult

Field of a Magnet & Magnet in a Uniform Field

A coil in the shape of an equilateral triangle of side $l$ is suspended between the pole pieces of a permanent magnet such that $\vec{B}$ 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

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Answer: (b)

$\vec{B}$ in the plane of the coil, so $\vec{m} \perp \vec{B}$ : $\tau = iAB$ .
Area of equilateral triangle $A = \frac{\sqrt{3}}{4}l^2 \Rightarrow \tau = \frac{\sqrt{3}}{4}l^2 iB$
$l^2 = \frac{4\tau}{\sqrt{3}Bi} \Rightarrow l = 2\left(\frac{\tau}{\sqrt{3}Bi}\right)^{1/2}$
So the answer is (b).

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