AP Physics C: E&M - Core Concepts & Calculations

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Coulomb's Law (Vector Form)

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Describes the electric force between two point charges: \(\mathbf{F}_{12}=k_e\,\frac{q_1q_2}{r^2}\,\hat{r}_{12}\), where \(\hat{r}_{12}\) points from charge 1 to charge 2. The sign of \(q_1q_2\) determines the direction: like charges repel (force along \(\hat{r}_{12}\)) and opposite charges attract (force opposite \(\hat{r}_{12}\)).

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Electric Field Definition

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Defined as the electric force per unit charge. Formula: **E = F / q0**. * **Units**: Newtons per Coulomb (N/C) or Volts per meter (V/m). * **Direction**: The direction of the force on a *positive* test charge. * **Superposition**: The net field is the vector sum of individual fields from all source charges.

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Electric Flux

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A measure of the number of electric field lines passing through a given area. Formula: **Phi_E = integral(E • dA)**. * For uniform E and flat surface: **Phi_E = E * A * cos(theta)**. * **dA**: Vector pointing normal to the surface, magnitude dA. * **Max Flux**: Field lines perpendicular to surface (theta = 0). * **Zero Flux**: Field lines parallel to surface.

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Gauss's Law

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Relates the net electric flux through a closed Gaussian surface to the enclosed charge. Formula: **oint(E • dA) = Q_enc / epsilon_0**. * **Use Case**: Symmetry (spherical, cylindrical, planar). * **Q_enc**: Net charge enclosed *inside* the surface only. Outside charges do not contribute to net flux. * **epsilon_0**: Vacuum permittivity (8.85 x 10^-12 C^2/N m^2).

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Electric Potential Energy (U)

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The work done by an external agent to bring a charge from infinity to a point without acceleration. Formula: **U = k_e * (q1 * q2 / r)**. * **System Property**: Belongs to the system of charges, not one charge. * **Reference**: U = 0 at r = infinity. * **Negative U**: Indicates a bound system (attractive force).