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Magnetism

Section: Physics

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Question : 35 of 46

Marks: +1, -0

A cylinder cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinity long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point O is given by

\frac{N}{12} \mu_a J

, then the value of N is _____.

[JEE Adv 2012 P1]

Your Answer:

Solution:

On the surface of the cylinder, the magnetic field is given by

\frac{\mu_0 J a}{2}

At a radial distance r outside, the magnetic field is given by

\frac{\mu_0 J a^2}{2r}

According to the principle of superposition, we have

B =

\frac{\mu_0 J a}{2} - \frac{\mu_0 J}{2\pi \left(\frac{3a}{2}\right)} \times \frac{\pi a^2}{4}

=

\frac{5 \mu_0 J a}{12}

⇒ N = 5

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