1. Understand the geometry

A current $I$ flows along the length of an infinitely long, straight, thin-walled cylindrical pipe.

This means the current is distributed symmetrically over the cylindrical surface and flows parallel to the axis of the pipe.

2. Use Ampere's law

Ampere's law states:

$\oint \vec{B}\cdot d\vec{l} = \mu_0 I_{\text{enc}}$

Because the arrangement is cylindrically symmetric, the magnetic field depends only on the distance $r$ from the axis and is tangential to circles centered on the axis.

So for a circular Amperian loop of radius $r$ coaxial with the pipe,

$B(2\pi r)=\mu_0 I_{\text{enc}}$

3. Consider points inside the pipe

For any point inside the thin-walled pipe, we take an Amperian circle with radius $r$ less than the pipe radius $R$.

Since all the current flows on the cylindrical wall at $r=R$, the current enclosed by the Amperian loop is:

$I_{\text{enc}}=0$

Therefore,

$B(2\pi r)=0 \implies B=0$

So the magnetic field is zero at every point inside the pipe.

4. Check the options

• A: "the magnetic field at all points inside the pipe is the same, but not zero"
  False, because the field inside is zero.

• B: "the magnetic field is zero only on the axis of the pipe"
  False, because it is zero everywhere inside, not only on the axis.

• C: "the magnetic field is different at different points inside the pipe"
  False, because the field is the same everywhere inside: zero.

• D: "the magnetic field at any point inside the pipe is zero"
  True.

5. Final answer

The correct option is:

$\boxed{\text{D}}$

6. Comparison with stored answer

Stored correct answer: $\text{D}$
My derived answer: $\text{D}$

They agree.