23.1 Electric Potential Energy:-Work done by a conservative force = deltaU = -(Ub-Ua) = Ua-Ub = Kb - Ka-Which derives the Work-Energy Theorem:Ka + Ua = Kb + Ub-Work in a uniform field = Fd = qEd-Work done by two point charges on each other = Integral of Fdr from a to bkq1q2*Integral(1/r^2) dr-Electric potential energy of two point charges = U = kq1q2/r-Electric potential energy w/ several pt. charges = U = ksum(qiqj/ri)23.2 Electric Potential:-Electric Potential = V = U/q0 [V or J/C]-Work from a to b/q0 = -deltaU/q0 = V_a - V_b-Potential of a w/ respect to b = work done by electric force when a UNIT charge moves from a to b.V_ab-Potential due to a single pt. charge = V = kq/r-Potential due to a collection of pt. charges = V = k*sum(qi/ri)-Potential due to a continuous distribution of charge = V = k*integral(dq/r)-Potential difference as an integral of E =V_a - V_b = integral a to b [Ecos(phi)dl] = integral a to b (E*dl)-U_a - U_b = qV_ab23.3: Calculating Electric Potential23.4: Equipotential Surfaces-3D surface on which the electric potential is the same at every point and U=q_0v is the same at every point-Electric field must be perpendicular to equipotential surface so it does not do work on a charge moving on the surface-When all charges are at rest, the surface of a conductor is ALWAYS an equipotential surface.23.5: Potential Gradient-E_vector is the negative gradient of VE = -grad_VNOTE**all these d's are partials =i(dV/dx + dV/dY + dV/dz)-For a radial E-Field:E_r = dV/dr