question_answer

Two long wire which are carrying same current I along x-axis and y-axis what is the value of magnetic field due to both wire at point \[P(3,4)\]:-

A)  \[\frac{{{\mu }_{0}}I}{12\pi }\]

B)  \[\frac{{{\mu }_{0}}I}{24\pi }\]

C)  \[\frac{{{\mu }_{0}}I}{48\pi }\]

D)  \[\frac{{{\mu }_{0}}I}{6\pi }\]

Correct Answer: B

Solution :

\[{{B}_{1}}=\frac{{{\mu }_{0}}I}{2\pi (4)}\odot \] \[{{B}_{2}}=\frac{{{\mu }_{0}}I}{2\pi (3)}\otimes \] \[B=\frac{{{\mu }_{0}}I}{2\pi }\left[ \frac{1}{3}-\frac{1}{4} \right]=\frac{{{\mu }_{0}}I}{24\pi }\]