Potential and Capacitance Assignment

(a) (b) + 2.5 mC ______rod_______ -2.5 mC

4.0cm 1.0cm 3.5 cm

There is a polarization / separation of charge in a 3.5 cm long rod (which we will consider one dimensional (and assume that all charge is at the very tips of the rod)). Point b in space is located 1.0 cm from the left end of the rod, and point a in space is located 4.0 cm left of point b.

1. What is the VOLTAGE between points a and b? Hint: voltage is potential difference. Hint on the hint: Use an equation for potential to find the potential at each point, and then take the difference between those two potentials. Another hint: the potential at either point will be the sum of the two potentials created by the two 5 micro Coulomb charges.
2. If a positive charge of 1.0 C moved from b to a, would its potential increase or decrease or stay the same? Would its potential energy increase, decrease, or stay the same (hint: is it "falling?")
3. Compare the changes a 0 C charge would experience compared to a 1.0 C charge. Would a 2.0 C charge experience more, less, or the same change of potential in the space it occupies when moving from b to a, compared to the 1.0 C charge? Would a 2.0 C charge experience more, less, or the same change of potential ENERGY when moving from b to a, compared to the 1.0 C charge? Support your answer to the energy part by citing an equation.
4. Now a negative charge moves from b to a. Think about the change in potential it experiences between those two places. Is this change positive, negative, or 0? Is its change in potential ENERGY positive, negative, or 0? (Hint: Is it "falling" or "rising?")

As of the beginning of 2021, google reports that the biggest available capacitor for a car audio system is 10.0 farads (this is very big). If this capacitor were charged to 120 volts, then the system turned off, and the capacitor allowed to discharge through a circuit with only 6.0 ohms of resistance for exactly one minute before you touched it wrong and shocked yourself, how many volts would you be shocked by? (Hints: -you might want to search course material for the term "time constant." -although referring to an equation would be useful, the math that is actually required is not too complicated.)

How much charge would be stored in the capacitor when there is 120V between the plates?

Bonus: How much electric potential energy is stored in the capacitor when it is charged to 120V?