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  • A current-carrying wire is placed in the grooves of an insulating semi-circular disc of radius 'R', as shown. The current enters at Point A and leaves from Point B. Determine the magnetic f

A current-carrying wire is placed in the grooves of an insulating semi-circular disc of radius 'R', as shown. The current enters at Point A and leaves from Point B. Determine the magnetic field at Point D.

 

Option: 1

\frac{\mu_{0}i}{8\pi R\sqrt{3}}


Option: 2

\frac{\mu_{0}i}{4\pi R\sqrt{3}}


Option: 3

\frac{\sqrt{3} \mu_{0}i}{4\pi R}


Option: 4

None of these


Answers (1)

best_answer

B_{1} = \frac{\mu_{0}i}{4 \pi(2R \sin 30\degree)} [\sin 60\degree]

        = \frac{\sqrt{3}\mu_{0}i}{8 \pi R }

B_{2} = \frac{\mu_{0}i}{4 \pi(2R \sin 60\degree)} [\sin 30\degree]

        = \frac{\mu_{0}i}{8 \pi R \sqrt{3}}

Now, 

B_{net} = B_{1} - B_{2}

            = \frac{3\mu_{0}i}{8 \pi R} - \frac{\mu_{0}i}{8 \pi R \sqrt{3}}

            = \frac{\mu_{0}i}{4 \sqrt{3}\pi R }

Posted by

Shailly goel

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