Question

4-7. (a) An element of wire of oriented length dil is moving with velocity u in a mag- netic field B. Show that the motional EMF developed in this element is given by (b) A conducting spherical shell of radius a and negligible thickness rotates with angular velocity ω ωez, în a uniform magnetic field described by B-Boer Calculate the EMF developed between one pole and a point on the equatorial circle.

Answer 1

(a) The mobile charge carriers (electrons) carried along within the wire are subject to the Lorentz force Fqux Blc Eq. . The work done on a charge q as it is pumped through the element is dW= F-dl, and the emf is defined as the work done per unit charge. Thus, dW u Note: There is a seeming paradox here because magnetic forces, being perpendicular to the displacement of a moving charge, can in fact do no work on the charge! When this primitive "generator" drives a current, the current experiences a magnetic force, and the agent causing the motion does the work against this force. (b) For the rotating spherical shell, dl

and the emf between pole and equator is 2c Positive charge is pumped from the poles to the equator-i.e., the equator is the "positive" terminal of the generator.

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