Question

3. A hollow cylinder of length $L$ and radius $a$ has a uniform charge density $\sigma$ on its surface. The cylinder rotates with angular frequency $\omega$ about its axis (the z-axis). a. What is the magnetic field, B, as a function of position inside the cylinder? You may ignore end effects; i.e., assume a location far from the ends and that $a << L$. b. What is the magnetic dipole moment m of the cylinder? c. Find the magnetic field B at large distances, $r >> L$.

          3. A hollow cylinder of length $L$ and radius $a$ has a uniform charge density $\sigma$ on its
surface. The cylinder rotates with angular frequency $\omega$ about its axis (the z-axis).
a. What is the magnetic field, B, as a function of position inside the cylinder?
You may ignore end effects; i.e., assume a location far from the ends and
that $a << L$.
b. What is the magnetic dipole moment m of the cylinder?
c. Find the magnetic field B at large distances, $r >> L$.

3. A hollow cylinder of length L and radius a has a uniform charge density σ on its
surface. The cylinder rotates with angular frequency ω about its axis (the z-axis).
a. What is the magnetic field, B, as a function of position inside the cylinder?
You may ignore end effects; i.e., assume a location far from the ends and
that a << L.
b. What is the magnetic dipole moment m of the cylinder?
c. Find the magnetic field B at large distances, r >> L.

Added by Tammy A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Shaiju T

Step 1

Ampere's law states that the line integral of the magnetic field around a closed loop is equal to the product of the current enclosed by the loop and the permeability of free space. In this case, since the cylinder is rotating, it can be considered as a current Show more…

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A hollow cylinder of length L and radius a has a uniform charge density Ï on its surface. The cylinder rotates with angular frequency Ï‰ about its axis (the z-axis). a. What is the magnetic field, B, as a function of position inside the cylinder? You may ignore end effects; i.e., assume a location far from the ends and that a << L. b. What is the magnetic dipole moment, m, of the cylinder? c. Find the magnetic field, B, at large distances, r >> L.