Lecture 2022-01-20 ✅

• Electric Flux through a surface is proportional to the charge inside of it.

Lecture 2022-01-25 ✅

• The net electric force through any closed surface depends only on the charge inside that surface.

• For an insulating sphere $S$ with radius $r$, you can treat the electric field at a point outside the sphere to be equivalent to the electric field created by a point charge centered at the sphere's center.

• Conductors don't have a charge inside of them.

Lecture 2022-01-27 ✅

• If you put a charge on a conductor it goes toward the outer surface.

• The electric field between two charged plates: $\frac{\sigma}{\varepsilon_0}$

Chapter 25 | Electric Potential

Lecture 2022-05-03 ✅

• A positive charge creates a positive electric potential around it.

• The formula for the electric potential $V$ at point $P$

  $$ V_P = k_e \sum_{i}{\frac{q_i}{r_i}} $$

• The change in potential energy is equal to the negative of the work done by the system. For a distance $d$ between two plates of opposite charge, with electric field $E$ flowing from one to the other, the work done is:

  $$ U_b - U_a = -W U_b - U_a = -qEd $$

• Electric potential $V$ is the electric potential energy $U$ per unit charge $q$. That is,

  $$ V = \frac{U}{q} $$

• Voltage (unit: Volts $V$)

  $$ \rm 1 ~ V = \frac{1 ~ J}{1 ~ C} $$

Chapter 27 | Current & Resistance

Link: Khan Academy "Resistors in Parallel"

• Resistors in Parallel

  • Formula: $R_{Parallel} = \frac{R_1 R_2}{R_1 + R_2}$

  • Resistors in parallel share the same voltage.

  • The equivalent resistance of a resistor in parallel always smaller than the smallest parallel resistor in the circuit.

• Resistors in Series

  • Formula: $R_{Series} = R_1 + R_2$

  • Resistors in series share the same current.

• Kirchoff's law states that the current through a circuit is equal to the sum of the currents through all the resistors in the circuit.

Miscellaneous

• Electric field lines are always perpendicular to the surface of the conducting material.

• If all charges are at rest, the electric field inside a conductor is zero. When you place a charge on a conductor, all of it goes to its outside surface. If there is a charge inside of a current, it means there must be a current flowing through the conductor.

• A Faraday's cage is a hollow, continuous surface (or mesh) made of a conductive material, used to block electromagnetic fields.

• Electromagnetic waves travel at the speed of light.

• An electromagnetic wave is transverse. $E$ and $B$ are perpendicular to one another, and both are perpendicular to the propagation of the wave.

Lecture 2022-02-01 ✅

• In-Class Questions:

  1. Question: What kind of Gaussian surface would we use to determine the electric field due to an insulating sphere?

     Answer: A sphere.

  2. Question: What kind of Gaussian surface would we use to determine the electric field due to an conducting sphere?

     Answer: A sphere.

  3. Question: What kind of Gaussian surface would we use to determine the electric field due to an infinite line of charge?

     Answer: A cylinder.

  4. Question: What kind of Gaussian surface would we use to determine the electric field due to an insulating cylinder?

     Answer: A cylinder.

  5. Question: What kind of Gaussian surface would we use to determine the electric field due to an infinite sheet of charge?

     Wrong Answer: An infinite sheet.

     Wrong! You need an infinite surface for a Gaussian.

     Correct Answer: Either cylinder or cube.

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