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Electric Potential Energy and Electric Potential Chapter 24 Preview of Today’s Class • Electric Potential Energy Difference • Electric Potential Energy • Electric Potential Difference • Electric Potential • Equipotential Surfaces Electric Potential Energy Difference Energy, ∆UE, to move a set of charges from initial to final state is the electric potential energy difference ∆ U E = force × distance = ∫ F • d x Charge moving in uniform electric field ∆ U E = E q x cos θ Units : N •C•m → N•m → J C ∆UE is work W done by ‘external agent’ (W=-Wsys) q1 q1 q2 q2 x Simple example Electric Potential Energy Energy, UE, is the electric potential energy of the configuration. It is same as electric potential energy difference but assumes the ‘move’ is for charges that are infinitely far apart to start with. ∞ U = UE = Uf – Ui =Uf, since Ui taken as zero ∞ q1 q2 q3 ∞ Electric Potential Energy of Charge Configuration Energy to assemble a group of charges U = U12 + U 23 + U13 q1 q2 q3 kq1q2 kq2 q3 kq1q3 = + + r12 r23 r13 What about positive and negatives? Electric Potential Difference (Property of the Field) Change in energy/charge, ∆V, to move distance d in electric field, E, is electric potential difference. ∆V = ∆U E q = work per charge ∆V = (force/charge) × distance = ∫Edx Units: N/C × m → N·m/C → J/C → volt + σd ∆V = ε0 ∆V = ? + + + + + - Electric Potential and Potential Difference With Point Charges Energy/charge, V, to move from infinity to a position in electric field, E. For a point charge: 1 kq kq kq 1 and ∆ V = V = − = kq − r r2 r1 r1 r2 + Sample Problems 17. (a) How far from a charge of +1.0 µC is a point with an electric potential value of 10 kV? (b) If the point were moved three times that distance, how much of a potential change would occur? Does it increase or decrease? 20. How much work is required to separate two charges (each -1.4 µC) completely if they are initially 8.0 mm apart?