question_answer

In the figure, what is the magnetic field at the point O   [MP PMT 2004]

A)            \[\frac{{{\mu }_{0}}I}{4\pi r}\]

B)            \[\frac{{{\mu }_{0}}I}{4\pi r}+\frac{{{\mu }_{0}}I}{2\pi r}\]

C)            \[\frac{{{\mu }_{0}}I}{4r}+\frac{{{\mu }_{0}}I}{4\pi r}\]

D)            \[\frac{{{\mu }_{0}}I}{4r}-\frac{{{\mu }_{0}}I}{4\pi r}\]

Correct Answer: C

Solution :

                   Magnetic field due to different parts are                           B1 = 0                    \[{{B}_{2}}=\frac{{{\mu }_{0}}}{4\pi }.\frac{\pi i}{r}\]¤                    \[{{B}_{3}}=\frac{{{\mu }_{0}}}{4\pi }.\frac{i}{r}\]¤            \[\therefore \ {{B}_{net}}={{B}_{2}}+{{B}_{3}}=\frac{{{\mu }_{0}}i}{4r}+\frac{{{\mu }_{0}}i}{4\pi r}\]