How superconductors produce strong magnetic field when they have the property of repelling magnetic field?
We must understand the cute difference here, friend Sharp. In superconducting stage ie at that temperature magnetic lines will not be allowed to pass through the material, but will be allowed through the coil. Through the material means through the solid medium. Through the coil means through space enclosed by the coil. At super conducting stage, the resistivity totally vanishes. So a large current can be passed through the coil (wire) and so intense magnetic field can be produced in the surrounding space. Because B = mu*n*i where mu is permeability of free space, n number of turns per unit length in case of a solenoid and i the current passing. So heavy current without any heat loss ie i^2R loss can be expected to go through the wire.
