Permeability of Free Space

State the meaning of permeability, write down the expression for the permeability of free space, and indciate how it was developed from the Biot-Savart Law. Draw the B-H characteristic for: a) a ferromagnetic material b) a non-ferromagnetic material and show how the permeability may be calculated from them.

Half-wave controlled rectifier circuit (Power Electronics)

I've attached jpegs that show the circuits that I'm working with. My problem is that I don't know how to find the values of Ct and Rt for a specific firing angle. What formulas are needed? Is the calculation affected by the fact that there are two different loads (see circuits 1 and 2 jpegs)? What process must I go through to find a firing angle of, say, 60 degrees in each case.

A problem on speed control of DC motor.

A separately excited dc motor is running at 500rpm, driving a load whose torque is proportional to the speed, the motor armature voltage is 220V and the armature current is 20A. What resistance should be inserted in the armature circuit to reduce the motor speed to 250rpm? The armature resistance is 1 ohm.