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Physics II - Midterm Revision

Proofread by Huỳnh Hà Phương Linh

TABLE OF CONTENTS

Chap 22

  • $Q = ne$
  • $\displaystyle \vec F = k_e\frac{q_1q_2}{r^2}\hat r$
  • $\displaystyle \vec E = \frac{\vec F}{q} \bigg[\frac{N}{C}\bigg]\bigg[\frac{V}{m}\bigg]$

Chap 23

  • $\displaystyle \vec E = k_e\int \frac{dq}{r^2} \hat r$

Gauss Law

  • $\displaystyle \phi_E = \oint_S \vec E.d\vec A = \frac{q_{in}}{\epsilon_0} \bigg[\frac{N.m^2}{C}\bigg]$

Field Due to a Spherically Symmetric Charge Distribution

  • $r > a:$ $\displaystyle E = \frac{Q}{4\pi\epsilon_0r^2}$
  • $r < a:$ $\displaystyle E = \frac{Qr}{4\pi\epsilon_0a^3}$

Field at a Distance from a Line of Charge

  • $\displaystyle E = \frac{2k_e\lambda}{r}$

Chap 24

  • $\displaystyle \Delta K = \int \vec F.d\vec s = \int q.\vec E.d\vec s$
  • $\displaystyle \Delta K + \Delta U = 0 \to \Delta U = -\Delta K = -\int q.\vec E.d\vec s$
  • $\displaystyle \Delta V = \frac{\Delta U}{q} = -\int\vec E.d\vec s$

Potential Difference in a Uniform Field

  • $\displaystyle \Delta V = E.d$

The potential difference between points A and B:

  • $\displaystyle V_B - V_A = k_eq\bigg[\frac{1}{r_B} - \frac{1}{r_A}\bigg]$
  • Choose $r_A \to \infty$ and $V_A = 0:$ $\displaystyle V = \sum_i \frac{kQ_i}{r_i}$
  • $\displaystyle E = -\frac{dV}{dx} \to F = -\frac{dU}{dx}$

Electric Potential for a Continuous Charge Distribution

  • $\displaystyle \Delta V = k_e \int \frac{dq}{r} = -\int_A^B \vec E.d\vec s$

Conductor in Electrostatic Equilibrium

  • $E_{inside} = 0$
  • $V_{inside} = const$
  • $\Delta V= 0$ between any two points on the surface.
  • Extra charges on the surface.
  • $\displaystyle E = \frac{\sigma}{\epsilon_0}$ (Nguyên lý hoạt động của cột ngư lôi)

Chap 25

  • $V_1 = V2$
  • $\displaystyle \frac{q_1}{R_1} = \frac{q_2}{R_2}$
  • $\displaystyle \frac{\sigma_1}{\sigma_2} = \frac{q_1}{q_2}\cdot\frac{R_2^2}{R_1^2}$

Capacitance

  • $\displaystyle C = \frac{Q}{\Delta V}$

Parallel Plate Capacitor

  • $\displaystyle E = \frac{\sigma}{\epsilon_0} = \frac{q}{A\epsilon_0}$
  • $\displaystyle \Delta V = E.d = \frac{q.d}{A\epsilon_0}$
  • $\displaystyle C = \frac{q}{\Delta V} = \frac{A\epsilon_0}{d}$

Capacitance of a Cylindrical Capacitor

  • $\displaystyle C = \frac{l}{2k_e\ln(b/a)}$

Capacitance of a Spherical Capacitor

  • $\displaystyle a \approx b: C \approx \frac{A.\epsilon_0}{d}$
  • $\displaystyle b \to \infty: C \approx 4\pi\epsilon_0a$

Capacitors in Parallel

  • $Q_{total} = Q_1 + Q2 = (C_1 + C_2).\Delta V$
  • $C_{total} = C_1 + C_2$
  • $\Delta V_1 = \Delta V_2 = \Delta V$

Capacitors in Series

  • $Q_1 = Q_2 = Q$
  • $\Delta V_{total} = \Delta V_1 + \Delta V_2$
  • $\displaystyle \frac{1}{C} = \frac{1}{C_1}+ \frac{1}{C_2}$

Energy Stored in a Capacitor

  • $dU = dq\cdot \Delta V$
  • $\displaystyle W = \frac{Q^2}{2C} = \frac{Q\Delta V}{2} = \frac{C\Delta V^2}{2}$

Dielectric

  • $\displaystyle C = \frac{\kappa\epsilon_0A}{d}$

Electric Dipole

  • $\vec\tau = \vec p\times\vec E$
  • $\vec p = q\cdot\vec d$
  • $U = -\vec p\cdot \vec E$

Chap 26

  • $\displaystyle I_{avg} = \frac{\Delta Q}{\Delta t} = \frac{n.q}{\Delta t} = \frac{\frac{n}{V}.V.q}{\Delta t} = n.A.q.v$

Ohm Law

  • $\displaystyle J = \sigma.E \to \frac{I}{A} = \sigma.\frac{\Delta V}{l} \to \frac{\Delta V}{I} = \frac{l}{\sigma.A} = R$
  • $\displaystyle \sigma = \frac{nq^2t}{m_e} = \frac{1}{\rho}$
  • $\displaystyle R = \frac{\rho\cdot l}{A}$
  • $\rho = \rho_0[1 + \alpha(T-T_0)] (\alpha >0: metal,\,\ \alpha < 0: semi \,\ conductor)$
  • $R = R_0[1+\alpha(T-T_0)]$

Electric Power (Joule - Lenz)

  • $\displaystyle P = I\cdot\Delta V = I^2\cdot R = \frac{\Delta V^2}{R}$