Physics

• Publisher: QuickStudy Reference Guides
• Year: 2009
• ISBN:
  9781423212744
• Topic: Sciences physiques
• Subtopic: Physique

Reference and outline to concepts in physics.

ELECTRICITY & MAGNETISM

1. Electric Fields & Electric Charge
   Examine the nature of the field generated by an electric charge and the forces between charges
   1. Coulomb, given the symbol C, is a measure of the amount of charge: 1 Coulomb = 1 amp • 1 sec e is the charge of a single electron: e = 1.6022 x 10^-19 C
   2. Coulomb’s Law for electrostatic force, Fcoul =

      1

      4πεo

      q1q2

      r^2

      r̂
   3. Electric Field, E, is the potential generated by a charge that produces F_coul on charge q_o:

      E =

      Fcoul qo

   4. Superposition Principle: The total F and E have contributions from each charge in the system: F = Σ F_i E = Σ E_i
2. Sources of Electric Fields: Gauss's Law
   1. Electric flux, Φ_e gives rise to electric fields and Coulombic forces
   2. Gauss’s Law:Φ_e = ∫ E · dA =

      Q

      εo

      The electric flux, Φ_e , depends on the total charge in the closed region of interest
3. Electric Potential & Coulombic Energy
   1. Coulombic potential energy is derived from Coulombic force using the following equation: U_coul = ∫ F_coul dr
      1. Coulombic Potential Energy: U_coul =

         1

         4πεo

         qq'

         r

      2. Coulombic Potential/Voltage
         1. The Coulomb potential, V(q), generated by q is obtained by dividing the U_coul by the test charge, q': U = V(q)q' V(q) =

            U

            q'

            =

            1

            4πεo

            q

            r

      3. For an array of charges, q_i, V_total = ΣV_i
   2. Potential for a Continuous Charge Distribution: V =

      1

      4πεo

      ∫

      dq

      r

   3. The Dielectric Effect
      1. Electrostatic forces and energies are diminished by placing material with dielectric constant l between the charges
      2. Voltage and electrostatic force (V & F) depend on the dielectric constant, k
      3. For a material with dielectric constant k : V(k) =

         1

         k

         V(vacuum) F(k) =

         1

         k

         F(vacuum)
4. Capacitance & Dielectrics
   1. A capacitor consists of two separated electrical conducting plates carrying equal and opposite charge. A capacitor stores charge/electrical potential energy
   2. Capacitance, C, is defined as the ratio of charge, Q, divided by the voltage, V, for a capacitor: C =

      Q

      V

      V is the measured voltage; Q is the charge
      1. Energy stored in a charged capacitor: U =

         ½Q^2

         C

         = ½QV = ½CV²
      2. Parallel plate capacitor, with a vacuum, with area A, and spacing d:
         1. Capacitance: C = ε_o

            A

            d

         2. Energy Stored: U = ½ε_oAdE²
         3. Electric Field: E =

            V

            d

            =

            Q

            εoA

      3. 
         Parallel plate capacitor, dielectric material with dielectric constant k, with area A, spacing d: C =

         kεoA

         d

         = kC₀ C₀ = vacuum capacitor
         1. Capacitors in Circuits: A group of capacitors in a circuit is found to behave like a single capacitor
         2. Capacitors in Series:

            1

            Ctot

            = Σ

            1

            Ci

         3. Capacitors in Parallel: C_tot = ΣC_i
   
5. Current & Resistance: Ohm’s Law
   1. Current & Charge: The current, I, measures the charge passing through a conductor over a time; total charge, Q: Q = I · t
   2. Ohm’s Law: Current density, J, is in proportion to the field; σ is called the conductivity: J = σE
   3. Resistance
      1. The resistance, R, accounts for the fact that energy is lost by electron conduction; resista...