Electric and Magnetic Fields

Homework 4 for EE 340 Date:_____________ ID:_______________ Name:________________________________________ We will cover the difference between capacitance and stored energy in the capacitor. 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 = ½ CV2 or ½ 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 = ½ CV2 or ½ 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 ½ CV2 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? Fig. 1 Fig. 2

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