Q146 / 180 · KCET 2020 · Physics
A long cylindrical wire of radius $R$ carries a uniform current $I$ flowing through it. The variation of magnetic field with distance $r$ from the axis of the wire is shown by
- A

- B

- Correct answerC

- D

Solution
Magnetic field due to long cylindrical wire of radius $R$ inside the cylinder at a distance $r < R$
$\begin{aligned}
& B_{\text {in }} &\left.=\frac{\mu_{0}}{2 \pi} \cdot \frac{I r}{R^{2}} \quad \text { [where, } I=\text { current }\right] \\
\therefore \quad & B_{\text {in }} & \propto r ...(i)
\end{aligned}$
Magnetic field outside the current carrying cylindrical wire of radius $R$ at a distance $r>R$ is given as
$B_{\mathrm{out}}=\frac{\mu_{0} I}{2 \pi r}$
i.e. $\quad B_{\text {out }} \propto \frac{1}{r}...(ii)$
From Eqs. (i) and (ii), graph between $B$ and $r$ drawn as


Hence, the correct answer is option: 'C'.