Introduction to Electrodynamics · Problem 7.47

Conservation Laws — David J. Griffiths

Physics · rotating-conducting-shell-emf

Problem

A perfectly conducting spherical shell of radius

a

rotates about the

z

axis with angular velocity

\omega

, in a uniform magnetic field

\mathbf{B} = B_0 \hat{z}

. Calculate the emf developed between the "north pole" and the equator. [Answer:

\frac{1}{2}B_0 \omega a^2

]