Unit 1: Electric Charges, Fields, and Gauss’s Law
Physics C: E&M · Unit 1 · Paper 1

Electric Charges, Fields, and Gauss’s Law 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.

Paper 1Paper 2Paper 3
Each paper is built from this unit’s 22 terms and is the same for everyone, so a teacher can assign “Unit 1, Paper 1” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 37 min 34 points0/17 attempted
1

Field of a finite line of charge

2

Gauss's law

3

Charge densities

4

Field on the axis of a charged ring

5

Flux through a closed surface with no enclosed charge

6

Charge on a conductor surface

7

Field of an infinite line of charge

8

Electric field of a point charge

9

Choosing a Gaussian surface

10

Field inside a uniformly charged insulating sphere

11

Gauss's law vs direct integration

12

Field inside a conductor in electrostatic equilibrium

Short answer 1. Define or explain: Symmetry arguments to eliminate components

3 pts

Short answer 2. Define or explain: Superposition of fields

3 pts

Short answer 3. Define or explain: Shielding

3 pts

Short answer 4. Define or explain: Coulomb's law in vector form

3 pts

Free response

10 pts

A solid insulating sphere of radius R carries a total charge Q distributed uniformly throughout its volume.

A. Derive an expression for the volume charge density of the sphere in terms of Q and R.

B. Using Gauss’s law, derive an expression for the magnitude of the electric field at a distance r from the center of the sphere, for r < R.

C. Using Gauss’s law, derive an expression for the magnitude of the electric field at a distance r from the center of the sphere, for r > R.

D. Describe the appearance of a graph of the electric field magnitude as a function of r, from r = 0 to r well beyond R, and verify that your two expressions agree at r = R.