question_answer

In the figure, what is the magnetic field at the point O  

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 \[{{B}_{1}}=0\] \[{{B}_{2}}=\frac{{{\mu }_{0}}}{4\pi }\cdot \frac{\pi i}{r}\,\odot \] \[{{B}_{3}}=\frac{{{\mu }_{0}}}{4\pi }\cdot \frac{i}{r}\,\odot \] \[\therefore \,\,\,\,\,\,\,\,\,{{B}_{net}}={{B}_{2}}+{{B}_{3}}=\frac{{{\mu }_{0}}i}{4r}+\frac{{{\mu }_{0}}i}{4\pi r}\]