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Magnetism

Section: Physics

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Question : 33 of 46

Marks: +1, -0

An infinite long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current density along its length. the magnitude of the magnetic field,

\overset{\rightarrow}{B}

as a function of the radial distance r from the axis is best represented by

[JEE Adv 2012 P2]

Solution:

Case 1: Inside the cavity, the magnetic field is given by B = 0.

Case 2: Outside the cylinder, the magnetic field is B =

\frac{\mu_0 I}{2\pi r}

.

In the shaded region shown in the figure, the magnetic field is calculated as

B =

\frac{\mu_0 I}{2\pi r(b^2-a^2)} \left(r - \frac{a^2}{r}\right)

At r = a, we have B = 0 and at r = b, we have

B =

\frac{\mu_0 I}{2\pi b}

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