Potential uniform magnetic induction

Figure 4-28. Classical Penning discharge with uniform magnetic induction and electrostatic trapping of electrons general schematic, distribution of electrostatic potential, and magnetie field along the diseharge axis.

In many cases the response to a uniform magnetic induction field, B, is required, when the vector potential can be written as A = X r, which automatically satisfies the Coulomb gauge condition, V.A = 0. The hamiltonian can then be reduced to the form... 

Faraday s law of induction, E = where E is the induced electric field, V the velocity of motion, and B the intensity of magnetic induction, is the basis for at least two types of electromagnetic flowmeters. In such flowmeters, a uniform magnetic induction is established transverse to the flow in a pipe and the flow of the metered fluid generates a potential difference at suitable detecting electrodes. 

Retaining also the second term ik -r in the expansion of leads to a spatially non-uniform vector potential and electric field, as well as to a non-vanishing magnetic induction and to an interaction with molecules via the magnetic dipole and electric quadrupole operators. 

A rod of length I = 10 cm is spinning in a uniform magnetic field with an induction fi = 0.4 T in the plane perpendicular to the induction force lines. The axis of rotation passes through one end of the rod. Determine the potential difference Acp inducted at ends of the rod if the rod rotates with frequency n = 16 sec. ... 

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