Question

1. We place two capacitors with identical ε and dimensions outlined in Fig. 1 under the same voltage (i.e. we apply the same voltage source). (a) Which capacitor has a larger capacitance and why? (b) Which capacitor has more voltage? This should be trivial. (c) Which capacitor has more charge? Please answer in terms of Q = CV. (d) Which capacitor stores more energy? You may discuss in terms of either U = 72 CV2 or 12 Q²/C. 2. We place two capacitors with identical ε and dimensions outlined in Fig. 2 with the same charge (i.e. we apply the same current source for the same time duration). (a) Which capacitor has a larger capacitance and why? (b) Which capacitor has more voltage? Please answer in terms of Q = CV. (c) Which capacitor has more charge? This should be trivial. (d) Which capacitor stores more energy? You may discuss in terms of either U = 72 CV2 or 12 Q²/C. (e) Was your answer to 2d the same as to 1d? Please justify. 3. What is the total energy volume density stored in a capacitor if you are forced to avoid using Q or V, but are allowed to use the uniform electric field E? Hint: starting from 7 CV? may be easiest here. 4. Consider a point charge near a grounded metal plate. Could the field around it be approximated by Coulomb's Law for an isolated point charge? If not, what sort of field should we consider instead?

Answer 1

For detailed solution refer to the image uploaded.

As per HOMEWORKLIB RULES, only 1st question needs to be answered in case of multiple questions.

For solving the first question we use equations for capacitance, charge across a capacitor & energy across a capacitor