We have an infinitely long solenoid of radius R along the z-axis. The solenoid is electrically neutral. The surface current density K is dependent in time, K(t)=Kocos(wt) Find the magnetic field B(s,t) produced for s<R (inside solenoid), s>R (outside solenoid), and the associated electric fields. I had first considered using Ampere's Law to find the magnetic field, but realized that since the current is not constant that I can't use it. But I'm not sure if this works with time-dependence, since it is technically still a constant in terms of position (x,y,z). Can Ampere's Law be applied here? Otherwise I don't really know how to approach the problem since the Biot-Savart Law seems to be too complicated. Also, shouldn't the magnetic field outside the solenoid be zero? And once I find out B, do I have to apply Maxwell's equations to find E? I'm sorry I don't have an elaborate attempt, I'm really pretty stuck on this question.