A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is:
A. maximum at either ends of the conductor and minimum at the midpoint
B. maximum at the axis of the conductor
C. minimum at the surface of the conductor
D. minimum at the axis of the conductor
E. same at all points in the cross-section of the conductor
Choose the **correct** answer from the options given below:
Answer: (D) D Only
By Ampère's law, inside the conductor (radius $R$, distance $r$ from the axis):
$$B = \frac{\mu_0 I r}{2\pi R^2}\quad (r\le R),\qquad B = \frac{\mu_0 I}{2\pi r}\quad (r\ge R)$$
So $B$ increases linearly from **zero at the axis** to its maximum at the surface, then falls off outside.
A: For a long conductor the field does not depend on position along its length in this way ✗. B ✗. C ✗ (surface is the maximum). D ✓. E ✗.
So D only.
Solution by Sreeraj P, M.Sc Physics