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

A coil in the shape of an equilateral triangle of side $l$ is suspended between the pole of a permanent magnet such that $B$ is in plane of the coil. If due to current $i$ in the triangle a torque $\tau$ acts on it, the side $l$ of the triangle is:
  1. $\frac{2}{\sqrt{3}}\left(\frac{\tau}{B i}\right)$
  2. $2\left(\frac{\tau}{\sqrt{3} B i}\right)^{1 / 2}$
  3. $\frac{2}{\sqrt{3}}\left(\frac{\tau}{B i}\right)^{1 / 2}$
  4. $\frac{1}{\sqrt{3}} \frac{\tau}{B i}$

Solution

Since $I=M B=(I A) B=I \frac{\sqrt{3}}{4} l^2 B$ $\Rightarrow \quad l=2\left(\frac{\tau}{\sqrt{3} B I}\right)^{1 / 2}$

Asked in: NEET 2005

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