Answer:
a)
b)
c)
d)
Explanation:
Capacitance of the capacitor,
a) Energy of the dielectric filed capacitor,
b) When the dielectric is pulled out halfway with the battery still connected to the capacitor, then it acts like 2 capacitors connected in parallel.
Let the capacitance of the half with no dielectric be and of the filled half be . Then,
Therefore, total capacitance
and,
c) Let us first calculate the charge stored in the previous configuration,
Now, the dielectric is completely removed. Then the new capacitance is,
Therefore, energy of the capacitor,
d) The work done to remove the dielectric will be the difference in the energies of the 2 configurations (half-filled and fully removed), that is,