Two wires of same lengths are shaped into a square and a circle. If they carry same current, then the ratio of their magnetic moments is

Step-by-step solution

Magnetic moment of a loop is given by p_m=I A where, I= current through the loop A= area of loop Perimeter of square should be equal to the circumference of circle, since wires have same length. Therefore, 4 a=2 r a= r 2 ...(i) In Fig. (i), magnetic moment of square loop is given by aligned & p_ m₁ =I (A₁ ) & p_ m₁ = I ^2 r^2 4 aligned [from Eq. (i)] ...(ii) In Fig. (ii), magnetic moment of circular loop is given by aligned & p_ m₂ =I (A₂ ) & p_ m₂ =I ( r^2 ) aligned ...(iii) From Eqs. (ii) and (iii), we get p_ m₁