Q.
In the adjacent figure is shown a closed path $P.$ A long straight conductor carrying a current $I$ passes through $O$ and perpendicular to the plane of the paper. Then which of the following holds good?
A) $\int_{P}^{}{\mathbf{B.dl} = 0}$
B) $\int_{P}^{}{\mathbf{B.dl} = \mu_{0}I}$
C) $\int_{P}^{}{\mathbf{B.dl} > \mu_{0}I}$
D) None of these
Explanation
(b) A long straight conductor carrying current $I$ passes through $O,$ then by symmetry, all points of the circular path are equivalent and hence the magnitude of magnetic field should be same at these points.
The circulation of magnetic field along the circle is
$\oint_{}^{}{\mathbf{B.dl} = \mu_{0}I}$ (using Ampere’s law)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.