To solve this problem, we need to analyze the magnetic field $B$ inside and outside a cylindrical conductor carrying a constant current.$\\$1. Inside the conductor $(d < R): \\$The magnetic field $B$ inside a cylindrical conductor is given by Ampère's Law:$\\ B = \frac{\mu_0 I d}{2 \pi R^2} \\$where $\mu_0$ is the permeability of free space, $I$ is the current, and $d$ is the distance from the center.$\\$This shows that $B$ is directly proportional to $d. \\$2. Outside the conductor $(d \geq R): \\$The magnetic field $B$ outside the conductor is given by:$\\ B = \frac{\mu_0 I}{2 \pi d} \\$This shows that $B$ is inversely proportional to $d. \\$3. Analyzing the options:$\\$• Option 1: Shows a decreasing curve starting from $R. \\$• Option 2: Shows a sharp decrease at $R. \\$• Option 3: Shows a linear increase up to $R$ and then a decrease.$\\$• Option 4: Shows a linear increase and then a constant value.$\\$The correct representation is Option 3, which shows:$\\$• A linear increase in $B$ from the center to $R. \\$• A decrease in $B$ beyond $R. \\$Therefore, the correct option is Option 3.