PYQ NEET- Moving Charges And Magnetism L-3

Question: From Ampere’s circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is#

A) Uniform and remains constant for both the regions.

B) A linearly increasing function of distance upto the boundary of the wire and then linearly decreasing for the outside region.

C) A linearly increasing function of distance $r$ upto the boundary of the wire and then decreasing one with $\frac{1}{r}$ dependence for the outside region.

D) A linearly decreasing function of distance upto the boundary of the wire and then a linearly increasing one of the outside region.

Answer: (C) A linearly increasing function of distance $r$ upto the boundary of the wire and then decreasing one with $\frac{1}{r}$ dependence for the outside region.#

Sol:#

Explanation For solid wire

Inside point $$ \begin{aligned} & B=\frac{\mu_0 I r^2}{R^2 \times 2 \pi r} \ & =\frac{\mu_0 I r}{R^2 \times 2 \pi} \ & B \propto r \end{aligned} $$

Outside point $$ \begin{aligned} & B=\frac{\mu_0 I}{2 \pi r} \ & B \propto \frac{1}{r} \end{aligned} $$