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

The torque τ is given byτ=mBsin⁡θ∴τ=iABsin⁡90∘ or τ=iAB ......(1)(∵m=iA)where A = area of triangle.To calculate A, consider fig.(8).A=12× Base × height =12×BC×AD Now AD=l2+(l/2)2=32l ∴A=12×l×(3/2)l=(3/4)l2Substituting the value of A in eq. (1), we getτ=i(3/4)l2B or l2=τ(Bi)×43l=2τ3Bi1/2