question_answer

A long straight wire of a circular cross-section (radius a) carries a steady curent I and the current I 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 :

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