Electric Potential unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Potential inside a conducting sphere
Equipotential surfaces
Potential energy of a charge pair
Potential from a graph of E vs x
Field and potential can be independently zero
Potential energy of a charge configuration
Potential of a charged conductor
Why field is the negative gradient
Sign of the potential integral
Work and potential difference
Electric potential of a point charge
Energy of assembling charges
Short answer 1. Define or explain: Field from a graph of V vs x
3 ptsShort answer 2. Define or explain: Why potential is easier than field
3 ptsShort answer 3. Define or explain: Electron volt
3 ptsShort answer 4. Define or explain: Potential inside a uniformly charged insulating sphere
3 ptsFree response
10 ptsA thin rod of length L lies along the x-axis with its near end a distance a from the origin. The rod carries a total charge Q distributed uniformly along its length. Point P is at the origin.
A. Derive an expression for the linear charge density of the rod in terms of Q and L.
B. By direct integration, derive an expression for the electric potential at point P due to the rod, taking the potential to be zero infinitely far away. Express your answer in terms of Q, L, a and physical constants.
C. Using your result from part B, derive an expression for the x-component of the electric field at point P.
D. Show that your expression from part C reduces to the expected result when a is very large compared with L, and interpret that limit physically.