Magnetic Effects Of Current Question 417

Question: A current of I ampere flows in a wire forming a circular arc of radius r metres subtending an angle $ \theta $ at the centre as shown. The magnetic field at the centre O in tesla is

Options:

A) $ \frac{{\mu_{0}}I\theta }{4\pi r} $

B) $ \frac{{\mu_{0}}I\theta }{2\pi r} $

C) $ \frac{{\mu_{0}}I\theta }{2r} $

D) $ \frac{{\mu_{0}}I\theta }{4r} $

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Answer:

Correct Answer: A

Solution:

[a] $ B=\frac{{\mu_{0}}I}{2r}\times \frac{\theta }{2\pi }=\frac{{\mu_{0}}I\theta }{4\pi r} $