Magnetic/electric fields problem?
E(x,y,z) = alpha [yi - xj]
could not be a result of static charges, but now we are equipped to account for moving charge. The local form of Faraday’s law (quoted below) describes how such an electric field can come from a time-varying magnetic field.
curl(E) = -d/dt (B)
Suppose the magnetic field that induces this electric field results from current passing through a solenoid with a coil density of n . At time t = 0, the current passing through the solenoid is I0, and it is decreasing with time.
a.Determine the orientation of the axis of the solenoid, in term of the x, y, and z axes.
b.Find an equation for the current in the solenoid as a function of time, in terms of a, n, and I0.