question_answer

Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment is                                                                           [DCE 2002]

A)            2 : p                                          

B)            p : 2

C)            p : 4                                          

D)            4 : p

Correct Answer: C

Solution :

                   Suppose length of each wire is l. \[r\propto \frac{1}{B}\] \[{{A}_{cirde}}=\pi {{r}^{2}}=\pi {{\left( \frac{l}{2\pi } \right)}^{2}}=\frac{{{l}^{2}}}{4\pi }\]                    \[\because \] Magnetic moment                    \[M=iA\]                                       \[\Rightarrow \frac{{{M}_{square}}}{{{M}_{cirde}}}=\frac{{{A}_{square}}}{{{A}_{cirde}}}\]            \[=\frac{{{l}^{2}}/16}{{{l}^{2}}/4\pi }\]\[=\frac{\pi }{4}\]