question_answer

A long straight wire of a circular cross section (radius a) carries a steady current l and the current l is uniformly distributed across this cross-section. Which of the following plots represents the variation of magnitude of magnetic field B with distance r from the centre of the wire?

A)           

B)            

C)

D)

Correct Answer: A

Solution :

(a) Magnetic field due to a long straight wire of radius a carrying current l at a point distant r from the centre of the wire is given as follows:             \[B=\frac{{{\mu }_{0}}lr}{2\pi {{a}^{2}}}\] for \[r<a\]             \[B=\frac{{{\mu }_{0}}l}{2\pi a}\] for \[r=a\]             \[B=\frac{{{\mu }_{0}}l}{2\pi r}\] for \[r>a\]             The variation of magnetic field B with distance r from the centre of wire is shown in the figure.