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Question
A long, cylindrical tube of inner and outer radii a and b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnitude filed at a point (a) just inside the tube (b) just outside the tube.
Solution
a) The magnetic field inside any conducting tube is always zero.
∴ Magnetic field just inside the tube is zero.
(b) Let the point outside the tube with distance b be P.
Consider an Amperian loop, as shown in the figure.
Length of the loop, l = \[2\pi \times b = 2\pi b\]
Current enclosed in the loop = i
On applying Ampere's law, we get
\[\int B . dl = \mu_0 i\]
\[ \Rightarrow B \times 2\pi b = \mu_0 i\]
\[ \Rightarrow B = \frac{\mu_0 i}{2\pi b}\]
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