* * * * * where:/stands for average value.
Delta delta, representing increment.
△S = area of semicircle
△t =2a ÷ v (moving the diameter 2a at a constant speed v)
So the formula of option D in your picture is correct.
2. In the process of moving from D to C, △S increases gradually and △φ increases.
So option a is correct.
3. Let the midpoint of the arc CD be m, and at the moment when C reaches the boundary (enters the magnetic field), E reaches the maximum.
Em=Ecm+Edm=B*a*v+B*a*v=2B*a*v
So option c is wrong.
* * * * * Interestingly, at the moment when C reaches the boundary (enters the magnetic field), E will suddenly drop from the maximum to 0.
Think about it. Why? This characteristic is called inductance effect in physics and is widely used in the fields of power and electronics.