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.
Electric field of a point charge
Gauss's law vs direct integration
Checking a field expression
Why symmetry is required for Gauss
Field of an infinite plane of charge
Field of a continuous charge distribution
Charge densities
Field on the axis of a charged ring
Field inside a conductor in electrostatic equilibrium
Field of a finite line of charge
Electric flux
Conductor with a cavity
Short answer 1. Define or explain: Shielding
3 ptsShort answer 2. Define or explain: Field inside a uniformly charged insulating sphere
3 ptsShort answer 3. Define or explain: Coulomb's law in vector form
3 ptsShort answer 4. Define or explain: Symmetry arguments to eliminate components
3 ptsFree response
10 ptsA solid insulating sphere of radius R = 0.20 m carries a total charge Q = 6.0 μC distributed uniformly throughout its volume.
Use Gauss’s law to derive expressions for the magnitude of the electric field at radius r for r < R and for r > R.
Evaluate the field at r = 0.10 m, at r = R, and at r = 0.40 m.
Describe a graph of E versus r from r = 0 out to r = 3R, identifying where the field is greatest.
Using V = −∫E·dl with V = 0 at infinity, derive the potential at the surface and at the center of the sphere, and evaluate both.
Explain how the field and potential expressions would change if the sphere were instead a conductor carrying the same total charge.