A cylinder of radius R and length L, with R« L, carries a uniform volume charge density p. The cylinder rotates about its symmetry axis with a constant angular velocity w. (a) Find the electric field for both inside (r < R) and outside (r > R) the cylinder, where r is the distance to the symmetry axis. L (b) Find the magnetic field both inside (r < R) and outside (r > R) the cylinder, where r is the distance to the symmetry axis. Hint: Think of this system as many layers of solenoid and apply Ampere's law.

A cylinder of radius R and length L, with R« L, carries a uniform volume charge density p. The cylinder rotates about its symmetry axis with a constant angular velocity w. (a) Find the electric field for both inside (r < R) and outside (r > R) the cylinder, where r is the distance to the symmetry axis. L (b) Find the magnetic field both inside (r < R) and outside (r > R) the cylinder, where r is the distance to the symmetry axis. Hint: Think of this system as many layers of solenoid and apply Ampere's law.