question_answer

            One of the two identical conducting wires of length L is bent in the form of a circular   loop and the other one into a circular coil. If the same current is passed in both, the ratio of the magnetic field at the central of the loop \[({{B}_{L}}),\,\,\,\,i.e.\,\,\,\frac{{{B}_{L}}}{{{B}_{C}}}\]will be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) \[\frac{1}{N}\]                                      

B) N     

C) \[{{N}^{2}}\]             

D)               \[\frac{1}{{{N}^{2}}}\]

Correct Answer: D

Solution :

    \[2\pi \,R=L\]              \[N2\pi \,r=L\]      \[R=\frac{L}{2\,\pi }\]             \[r=\frac{L}{N.2\,\pi }\]   \[{{B}_{L}}\,\,=\,\,\frac{{{\mu }_{0}}I\,.\,2\pi }{2.\,L}\]                  \[{{B}_{c}}\,\,=\,\,\frac{{{\mu }_{0}}.NIN\,.\,2\pi }{2.\,L}\] \[\frac{{{B}_{L}}}{{{B}_{C}}}\,\,=\,\,\frac{\frac{{{\mu }_{0}}I2\,\pi }{2\,L}}{\frac{{{\mu }_{0}}.{{N}^{2}}I\,.\,2\pi }{2.\,L}}=\frac{1}{{{N}^{2}}}\] Option is correct.