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) \[\frac{1}{2}\left( \frac{{{\mu }_{0}}I}{2R} \right)\]
Correct Answer: A
Solution :
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.
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