Electric Charges, Fields, Gauss’s Law & Current: Physics Review
Electric Charges, Fields, Gauss’s Law and Current
The following notes cover the essential formulas, variables and problem-solving strategies for electric charges, electric fields, Gauss’s law, and current and resistance.
Variables and Definitions
- \(q, Q\) = charge (C)
- \(r\) = distance (m)
- \(\hat{r}\) = unit vector pointing away from source
- \(\lambda\) = linear charge density (C/m)
- \(\eta\) = surface charge density (C/m²)
- \(\rho\) = volume charge density (C/m³) or resistivity (Ω·m), depending on context
- \(\sigma\) = conductivity (Ω⁻¹·m⁻¹)
- \(A\) = area (m²)
- \(\vec{A} = A\hat{n}\) = area vector with outward normal \(\hat{n}\)
- \(\Phi_e\) = electric flux (N·m²/C)
- \(Q_{\text{in}}\) = enclosed charge (C)
- \(I\) = conventional current (A)
- \(i_e\) = electron current (electrons/s)
- \(J\) = current density (A/m²)
- \(v_d\) = drift speed (m/s)
- \(n_e\) = conduction-electron number density (m⁻³)
- \(\tau\) = mean time between collisions (s)
- \(R\) = resistance (Ω)
- \(L\) = length (m)
- \(\Delta V\) = potential difference (V)
Electric Charges and Forces
The Charge Model
Electric phenomena come from a property of matter called charge. There are exactly two kinds: positive and negative. Like charges repel; opposite charges attract. Charging means transferring electrons from one object to another. Protons are locked in nuclei and never move between objects. Charge is conserved and quantized:
\(q = (N_p – N_e)e\), where \(N_p\) = number of protons, \(N_e\) = number of electrons, and \(e = 1.60 \times 10^{-19}\) C.
An object is neutral when \(N_p = N_e\), not when it has