Dr. Munley explained this. A search might turn up his paper. The electrons move radially due to Lorentz force. As the disk rotates, the circuit path traced is a pie sector shape. One terminal of the ammeter is on the center spindle, with the other terminal a peripheral contact, i.e. a brush type connection. As the electrons move they sweep out an area increasing with angle theta, which equals omega*t, where omega is angular speed.
The area of the filamentary circuit, times the constant flux density B, equals the flux phi. Although B is static, phi is time changing in proportion to time to the 1st power. Since emf = -d(phi)/dt, the emf is the 1st derivative of flux wrt time. But time is raised to the 1st power, so emf is a constant, nonvarying w/ time. Observation affirms this, that the induced emf/current is indeed dc.
Flux phi equals flux density B times area. If B varies we have induction. If B is static but area A varies, we have induction. A variation of phi wrt time is needed for induction to happen. The phi variation is usually due to B variation, i.e. area A is usually fixed in xfmrs, generators, motors, solenoids, etc. But a Faraday disk is a case where the reverse happens, fixed B, varying A. Since phi is the product of the 2, phi varies in time, hence induction occurs.
Did I help? I will clarify if needed.
Claude
