Magnetic Effects of Current and Magnetism Part 3

Concept:Ampère's law states that the line integral of magnetic field around a closed loop equals $\mu_0$ times the current enclosed.For a uniform current distribution, the field depends only on radial distance from the axis.Explanation:Consider a long cylindrical conductor of radius $R$ carrying total current $I$ uniformly.Current density is $J = \frac{I}{\pi R^2}$.Inside the conductor ($r < R$): pick an Amperian loop of radius $r$ on the axis.Current enclosed: $I_{\text{enc}} = J \cdot \pi r^2 = \frac{I r^2}{R^2}$.By Ampère's law: $B (2\pi r) = \mu_0 I_{\text{enc}} = \mu_0 \frac{I r^2}{R^2}$.So $B = \frac{\mu_0 I r}{2\pi R^2}$ — increases linearly with $r$.At the axis ($r=0$), $B=0$ (minimum). Statement D is correct.Outside the conductor ($r > R$): loop encloses total current $I$.$B (2\pi r) = \mu_0 I$ → $B = \frac{\mu_0 I}{2\pi r}$ — decreases with $r$.Maximum at surface ($r=R$); therefore statement C (minimum at surface) is false.Statement B (maximum at axis) is false because $B=0$ at axis.Field varies with $r$, not uniform; statement E is false.The distribution depends on radial distance, not axial position; statement A is false.Thus only statement D is correct.Answer:Option D: D Only.