3.3.1 Potential Energy in a System of Charges If a system of charges is assembled by an external agent,thenAU=-W=+W.That is, the change in potential energy of the system is the work that must be put in by an external agent to assemble the configuration.A simple example is lifting a mass m through a height h.The work done by an external agent you,is +mgh (The gravitational field does work -mgh).The charges are brought in from infinity without acceleration i.e.they are at rest at the end of the process.Let's start with just two charges g and g2.Let the potential due to g at a point P be V(Figure 3.3.2). 92 12， 9○ Figure 3.3.2 Two point charges separated by a distance r2. The work W,done by an agent in bringing the second charge g2 from infinity to P is then W2=g2.(No work is required to set up the first charge and W=0).Since =g/4z2,where ri2 is the distance measured from g to p,we have 19192 U2=W=4π (3.3.5) If g and g2 have the same sign,positive work must be done to overcome the electrostatic repulsion and the potential energy of the system is positive,U20.On the other hand,if the signs are opposite,then U2 due to the attractive force between the charges. P 23 '12 93 91 13 Figure 3.3.3 A system of three point charges. To add a third charge g3 to the system(Figure 3.3.3),the work required is 3-83.3.1 Potential Energy in a System of Charges If a system of charges is assembled by an external agent, then∆U W = − = +Wext . That is, the change in potential energy of the system is the work that must be put in by an external agent to assemble the configuration. A simple example is lifting a mass m through a height h. The work done by an external agent  you, is +mgh (The gravitational field does work ). The charges are brought in from infinity without acceleration i.e. they are at rest at the end of the process. Let’s start with just two charges and . Let the potential due to at a point be (Figure 3.3.2). −mgh 1 q 2 q 1 q P V1 Figure 3.3.2 Two point charges separated by a distance . 12 r The work done by an agent in bringing the second charge from infinity to P is then . (No work is required to set up the first charge and ). Since W2 2 q W q 2 = 2 V1 1 W = 0 1 1 0 12 V q = / 4πε r , where is the distance measured from to P, we have 12 r 1 q 1 2 12 2 0 12 1 4 q q U W πε r = = (3.3.5) If and q 1 q 2 have the same sign, positive work must be done to overcome the electrostatic repulsion and the potential energy of the system is positive, . On the other hand, if the signs are opposite, then due to the attractive force between the charges. 12 U > 0 12 U < 0 Figure 3.3.3 A system of three point charges. To add a third charge q3 to the system (Figure 3.3.3), the work required is 3-8