Chapter 25: Electric Potential

• Possibility to define electric potential energy: The electric force is conservative.
   
• Electric potential energy: The negative of the work done by the electric force when a charge is moved (along any path) from a reference point O to a given point P, U = –W_PO. (The reference point can be arbitrarily chosen in any given problem, and it is often convenient to choose it at infinity.)
   
• Electric potential: Defined as V = U/q = –W_PO/q .
  
• Units: New unit for an electric field, 1 N/C = 1 V/m. Energy unit for particles, 1 eV = 1.60 × 10^–19 J.
   
• Equipotential surfaces: The general concept; How to draw them for simple charge arrangements; How they provide information on the direction and magnitude of the electric field.
   
• Calculating the potential from the field: In general, integrate

V(P) = –∫ E · ds . 

• Potential due to a point charge: From the electric field, at choosing V = 0 at infinity,

V = k q/r ,   so the potential energy of a 2-point-charge system is   U = k q₁q₂/r .

• Potential due to a charge distribution: Add the single-charge contributions, or set up an integral,

V = k ∫ dq/r .

• Calculating the field from the potential: In any direction s (for example, x, y, or z),

E_s = –∂V/∂s . 

• Potential on a charged insulator: Because the electric field must be zero inside the conductor, without current flows, the potential is constant throughout the conductor. (Remember that there can be a field and a charge density only on the surface.)