In situation (a), the power supply is maintaining a fixed potential difference between the plates, so the electric field between the plates must decrease when a dielectric is inserted. In situation (b), the capacitor is disconnected from the power supply, so the electric field between the plates remains constant when a dielectric is inserted.
When a sheet of dielectric is inserted between the plates of a parallel-plate capacitor connected to a power supply that maintains a fixed potential difference, the following changes occur:
(i) The electric field between the plates decreases. This is because the dielectric polarizes, creating an electric field that opposes the original electric field. The new electric field is given by E = V/dK, where E is the electric field, V is the potential difference, d is the plate separation, and K is the dielectric constant. Since K is greater than 1, the new electric field is less than the original electric field.
(ii) The energy stored in the capacitor decreases. This is because the electric field has decreased, and the energy stored in a capacitor is given by U = 1/2CV^2. Since the potential difference remains constant, the energy stored in the capacitor is proportional to the electric field.
Part (b):
When a charged parallel-plate capacitor is disconnected from a power supply and a dielectric is inserted between the plates, the following changes occur:
(i) The electric field between the plates decreases. This is for the same reason as in part (a).
(ii) The magnitude of charge on each plate remains constant. This is because the capacitor is disconnected from the power supply, and there is no current to change the charge on the plates.
(iii) The energy stored in the capacitor decreases. This is for the same reason as in part (a).