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

    Figure
  • B

    Figure
  • Correct answer
    C

    Figure
  • D

    Figure

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
Figure

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

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