A) \[\frac{{{\mu }_{0}}I}{R}\]
B) \[\frac{{{\mu }_{0}}I}{2R}\]
C) \[\frac{2{{\mu }_{0}}I}{R}\]
D) \[\frac{3{{\mu }_{0}}I}{8R}\]
Correct Answer: D
Solution :
For a loop, magnetic induction at centre \[B=\frac{{{\mu }_{0}}}{4\pi }\times \frac{2\pi I}{R}\] When loop subtends angle\[\theta \] at centre, then \[B=\frac{{{\mu }_{0}}}{4\pi }\times \frac{\theta I}{R}\] In the given problem\[\theta =\frac{3\pi }{2}\] \[\therefore \] \[B=\frac{{{\mu }_{0}}}{4\pi }\times \frac{3\pi }{2}\times \frac{I}{R}\] \[=\frac{3{{\mu }_{0}}I}{8R}\]
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