A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field, B with the distance, d from the centre of the conductor, is correctly represented by the figure [2019]

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Solution

Q.
A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field, B with the distance, d from the centre of the conductor, is correctly represented by the figure [2019]

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Ans.
(4)

Magnetic field due to long solid cylindrical conductor of radius $R$ ,

(i) For $d < R,$ $I' = \frac{I d^{2}}{R^{2}}$

   $\int \vec{B} \cdot d \vec{l} = μ_{0} I' \Rightarrow B (2 π d) = \frac{μ_{0} I d^{2}}{R^{2}} \Rightarrow B = \frac{μ_{0} I d}{2 π R^{2}}$

$∴$ $B \propto d$

(ii) For   $d = R,$    $B = \frac{μ_{0} I}{2 π R}$ (maximum)

(iii) For   $d > R,$ $B = \frac{μ_{0} I}{2 π d} \Rightarrow B \propto \frac{1}{d}$

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