Gravitationally coupled electromagnetic systems and quantum interference

The modification of the magnetic field produced by a solenoid, carrying current from a battery of constant EMF, due to their relativistic coupling to the gravitational field is obtained, using a general relativistic generalisation of Ohm's law. The corresponding phase shift in the Aharonov-Bohm effect due to the magnetic flux in the quantum interference of two coherent beams and in a superconducting interferometer, which uses the DC Josephson effect is computed. The effect of the gravitational field on the AC Josephson effect is also studied. It is shown that the ratio of emission frequencies of radiations from two Josephson junctions in parallel, separated by a height X, is (1-gX/c 2 ).