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Question
A long, cylindrical wire of radius b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnetic field at a point inside the wire at a distance a from the axis.
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Solution
Given:
Magnitude of current = i
Radius of the wire = b
For a point at a distance a from the axis,
Current enclosed,
\[i' = \frac{i}{\pi b^2} \times \pi a^2\]
By Ampere's circuital law,
\[B \times 2\pi a = \mu_0 \frac{i}{\pi b^2} \times \pi a^2 \]
\[ \Rightarrow B = \frac{\mu_0 ia}{2\pi b^2}\]
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