Unit 1: Electrostatics and Gauss's Law

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Big Ideas:
1. Like charges repel while opposite charges attract.
2. Electric fields exert force on charged particles.
3. Gauss's Law enables one to easily determine the strength of an electric field in some cases.  

Learner Objectives (as published by the College Board):
1. Students should understand the concept of electric charge, so they can:
A. Describe the types of charge and the attraction and repulsion of charges.
B. Describe polarization and induced charges.

2. Students should understand Coulomb's Law and the principle of superposition, so they can:
A. Calculate the magnitude and direction of the force on a positive or negative charge due to other specified point charges.
B. Analyze the motion of a particle of specified charge and mass under the influence of an electrostatic force.

3. Students should understand the concept of electric field, so they can:
A. Define it in terms of the force on a test charge.
B. Describe and calculate the electric field of a single point charge.
C. Calculate the magnitude and direction of the electric field produced by two or more point charges.
D. Calculate the magnitude and direction of the force on a positive or negative charge placed in a specified field.
E. Interpret an electric field diagram.
F. Analyze the motion of a particle of specified charge and mass in a uniform electric field.

5. Students should understand the relationship between electric field and electric flux, so they can:
A. Calculate the flux of an electric field through an arbitrary surface or of a field uniform in magnitude over a Gaussian surface and perpendicular to it.
B. Calculate the flux of the electric field through a rectangle when the field is perpendicular to the rectangle and a function of one coordinate only.
C. State and apply the relationship between flux and lines of force.

6. Students should understand Gauss's Law, so they can:
A. State the law in integral form, and apply it qualitatively to relate flux and electric charge for a specified surface.
B. Apply the law, along with symmetry arguments, to determine the electric field for a planar, spherical, or cylindrically symmetric charge distribution.
C. Apply the law to determine the charge density or total charge on a surface in terms of the electric field near the surface.

7. Students should be able to use the principle of superposition to calculate by integration:
A. The electric field of a straight, uniformly charged wire.
B. The electric field and potential on the axis of a thin ring of charge, or at the center of a circular arc of charge.
C. The electric potential on the axis of a uniformly charged disk.

8. Students should know the fields of highly symmetric charge distributions, so they can:
A. Identify situations in which the direction of the electric field produced by a charge distribution can be deduced from symmetry considerations.
B. Describe qualitatively the patterns and variation with distance of the electric field of oppositely-charged parallel plates, a long, uniformly-charged wire, or a thin cylindrical or spherical shell.
C. Use superposition to determine the fields of parallel charged planes, coaxial cylinders, or concentric spheres.