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Physics Chapter 23: Electric Potential and Energy

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  • Letter representing electric charge
    Electric charge is represented by the letter \(q\) or \(Q\).
  • SI unit of electric charge
    Electric charge is measured in coulombs, abbreviated as C.
  • Letter representing electric field
    Electric field is represented by the letter \(E\).
  • SI unit of electric field
    Electric field is measured in newtons per coulomb (NC) or volts per meter (Vm).
  • Letter representing work
    Work is represented by the letter \(W\).
  • SI unit of work
    Work is measured in joules, abbreviated as J.
  • Letter representing electric potential energy
    Electric potential energy is represented by the letter \(U\).
  • SI unit of electric potential energy
    Electric potential energy is measured in joules (J).
  • Letter representing electric potential
    Electric potential is represented by the letter \(V\).
  • SI unit of electric potential
    Electric potential is measured in volts, abbreviated as V.
  • Equation relating work done by a conservative force to potential energy
    \(W = -\Delta U\) defines the work done by a conservative force as the negative change in potential energy.
  • Equation for electric potential energy of two point charges
    \(U = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r}\) gives the electric potential energy between two point charges.
  • Equation for electric potential due to a point charge
    \(V(P) = \frac{1}{4 \pi \epsilon_0} \frac{q}{r}\) defines the electric potential at point P due to a point charge q.
  • Reference point where electric potential is zero for point charges
    Electric potential \(V = 0\) is defined at infinite distance: \(V_r = 0 \text{ as } r \to \infty\).
  • Equation to determine electric potential from electric field
    \(\Delta V = V_{final} - V_{initial} = - \int_{initial}^{final} \vec{E} \cdot d\vec{l}\) relates electric potential difference to the electric field.
  • Equation to determine electric field from electric potential
    \(E_x = -\frac{\partial V}{\partial x}\) gives the electric field component from the spatial derivative of electric potential.
  • Relation between electric field and potential gradient
    \(\vec{E} = - \nabla V\) shows that electric field is the negative gradient of electric potential.
  • Equation relating change in electric potential energy to change in electric potential
    \(\Delta U = q \Delta V\) relates the change in electric potential energy to the charge and change in potential.
  • Equation defining kinetic energy of a particle
    \(K = \frac{1}{2} m v^2\) defines the kinetic energy of a particle with mass m and speed v.
  • Conservation of energy equation including electric potential energy
    \(K_A + U_A = K_B + U_B \quad \text{with} \quad U = qV\) expresses conservation of mechanical energy including electric potential energy.