Question

A current $I$ enters a circular coil of radius $R$ branches into two parts and then recombines as shown in the circuit diagram.The resultant magnetic field at the centre of the coil is

• A. $zero$
• B. $ \frac{{{\mu }_{0}}I}{2R} $
• C. $ \frac{3}{4}\left( \frac{{{\mu }_{0}}I}{2R} \right) $
• D. $ \frac{1}{4}\left( \frac{{{\mu }_{0}}I}{2R} \right) $
• E. $ \frac{1}{2}\left( \frac{{{\mu }_{0}}I}{2R} \right) $

Answer 1

Answer: (A)

Magnetic field at B
$ {{B}_{1}}=\frac{{{\mu }_{0}}}{2\pi }\frac{I\Delta I}{r} $
Magnetic field at A
$ {{B}_{2}}=\frac{{{\mu }_{0}}}{2\pi }\frac{I\Delta I}{r} $
The resultant magnetic field at the centre
$ |{{B}_{A}}|-|{{B}_{B}}|=0 $
So magnetic field becomes zero.