First slide

Ampere's circuital law

Question

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

Moderate

A
B
C
D

Solution

Magnetic field due to long solid cylindrical conductor of radius R
$(i) For d < R, I^{'} = \frac{{Id}^{2}}{R^{2}} \int \vec{B} \cdot d \vec{l} = μ_{0} I^{'} \Rightarrow B (2 πd) = \frac{μ_{0} {Id}^{2}}{R^{2}} \Rightarrow B = \frac{μ_{0} Id}{2 {πR}^{2}} ∴ B \propto d (ii) For d = R, B = μ_{0} I / 2 πR (maximum) (iii) For d > R, B = μ_{0} I / 2 πd \Rightarrow B \propto 1 / d .$

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