A long upright solenoid of radius 30 mm and 5000 turns per meter is placed inside another long upright solenoid, this one of radius 80mm and 5000 turns per meter. Each solenoid has a current that is steadily increasing at a rate of 4A/s and the currents goes counterclockwise (so the magnetic fields point up). For quasistatic approximations and Faraday's Law for an Amperian loop, find the induced electric field. You may assume the induced electric field goes in horizontal circles and its strength depends on radius.
a) Find the induced electric field inside the inner solenoid, as a function of r, distance from the axis.
b) Find the induced electric field between the solenoids, as a function of r, distance from the axis.
c) Find the induced electric field outside the solenoids, as a function of r, distance from the axis.
d) Looking at the fields from above do they go clockwise or counterclockwise? Why?
e) What would change if currents were reversed (i.e. the magnetic fields now point down, and the current is decreasing at the rate of 4A/s so the magnetic fields are getting weaker)?