JEE Main & Advanced Physics Electro Magnetic Induction JEE PYQ-Electro Magnetic Induction

If in a circular coil A of radius R, current j is flowing and in another coil B of radius 2 R, a current 2 i is flowing, then the ratio of the magnetic fields, \[{{B}_{A}}\] and \[{{B}_{B}}\] produced by them will be [AIEEE 2002]

A) 1

B) 2

C) \[1/2\]

D) 4

Correct Answer: A

Solution :

[a] Magnetic field in circular coil A is \[{{B}_{A}}=\frac{{{\mu }_{0}}\,Ni}{2\,R}\] where, R is radius and \[i\] is current flowing in coil.

Similarly, \[{{B}_{B}}=\frac{{{\mu }_{0}}N(2i)}{2.\,(2R)}=\frac{{{\mu }_{0}}Ni}{2R}\]

\[\Rightarrow \] \[\frac{{{B}_{A}}}{{{B}_{B}}}=\frac{1}{1}=1\]