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Chapter 15: Problem 167

A current \(I\) flows along the length of an infinitely long, straight, thin- walled pipe. Then [2007] (A) the magnetic field at all points inside the pipe is the same, but not zero. (B) the magnetic field is zero only on the axis of the pipe. (C) the magnetic field is different at different points inside the pipe. (D) the magnetic field at any point inside the pipe is zero.

Short Answer

Expert verified
The correct answer is, (D) the magnetic field at any point inside the pipe is zero.

Step by step solution

01

Understanding Ampere's circuital law

Ampere's circuital law relates current and magnetic field around a closed path in the following way: The integral of magnetic field (B) around any closed path equals to \(\mu_0\) times the current flowing through the area enclosed by the path.
02

Analyze the given situation using the law

The given situation of a straight, thin-walled pipe carrying uniform current `I` along the length is compliant with the assumption of Ampere's law. Since the pipe is infinitely long and thin walled, the current is flowing uniformly throughout.
03

Determine the magnetic field inside the pipe

Since the current is uniformly distributed and is flowing through the entire cross-section, according to Ampere's law, the magnetic field inside the pipe would be zero.
04

Compare the findings with the options

The finding in step 3 confirms only option (D) which says the magnetic field at any point inside the pipe is zero.

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