Fields, losses and forces due to moving current distributions coaxial with a cylindrical conductor

An exact mathematical solution has been obtained for the quasistationary electromagnetic field of a circular current loop coaxial with a conducting circular cylinder in uniform relative motion with respect to each other. The vector magnetic potential corresponding to a filamentary loop carrying a variable with time current is determined by applying the method of separation of variables. Expressions for the fields outside and inside the cylindrical conductor, the eddy-current distribution, the power loss and the interaction force are derived directly from the vector potential. The fields due to practical current coils are obtained by integration from the results for the filamentary loop. An approximate simple formula is presented for a loop carrying direct current at high velocities. The analysis performed is relevant to the design and operation of magnetic devices with metallic cores in motion, linear electrical machines and electromagnetic launching systems.