Walker, Halliday & Resnick — Maxwell's Equations; Magnetism of Matter: Problem 36

36 Assume that an electron of mass \(m\) and charge magnitude \(e\) moves in a circular orbit of radius \(r\) about a nucleus. A uniform magnetic field \(\vec{B}\) is then established perpendicular to the plane of the orbit. Assuming also that the radius of the orbit does not change and that the change in the speed of the electron due to field \(\vec{B}\) is small, find an expression for the change in the orbital magnetic dipole moment of the electron due to the field.