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reminder Quiz Quiz next Wednesday 8:00am 8:50 am Refer to course website for exam location No make-up quiz! 1 conceptual and 2 numerical problems Coverage: Chapter 19 Preparation: concentrate on L, R and HW problems as well as textbook examples; read the textbook Student help center for PHYS102 is open. 915 Disque Hall Hours: 10am-5pm M,Tue,W,Thu 1 Electric Potential The potential energy per unit charge, U/qo, is the electric potential The potential is independent of the value of qo The potential has a value at every point in an electric field U The electric potential is V qo 2 Work and Electric Potential The electric potential at an arbitrary point due to source charges equals the work required by an external agent to bring a test charge from infinity to that point divided by the charge on the test particle Assumes a charge moves in an electric field without any change in its kinetic energy The work performed on the charge is W = V = q V 3 Units 1 V = 1 J/C V is a Volt It takes one Joule of work to move a 1 Coulomb charge through a potential difference of 1 Volt In addition, 1 N/C = 1 V/m This indicates we can interpret the electric field as a measure of the rate of change with position of the electric potential 4 Electron-Volts Another unit of energy that is commonly used in atomic and nuclear physics is the electronvolt One electron-volt is defined as the energy a charge-field system gains or loses when a charge of magnitude e (an electron or a proton) is moved through a potential difference of 1 volt 1 eV = 1.60 x 10-19 J 5 Potential Difference in a Uniform Field The equations for electric potential can be simplified if the electric field is uniform: VB - VA = V = - B A r r B E ds = -E ds = -Ed A The negative sign indicates that the electric potential at B is lower than at point A 6 Energy and the Direction of Electric Field When the electric field is directed downward, point B is at a lower potential than point A When a positive test charge moves from A to B, the charge-field system loses potential energy V = U = qo U = -q0 Ed 7 More About Directions A system consisting of a positive charge and an electric field loses electric potential energy when the charge moves in the direction of the field An electric field does work on a positive charge when the charge moves in the direction of the electric field The charged particle gains kinetic energy equal to the potential energy lost by the charge-field system Another example of Conservation of Energy 8 Directions, cont If qo is negative, then U is positive A system consisting of a negative charge and an electric field gains potential energy when the charge moves in the direction of the field In order for a negative charge to move in the direction of the field, an external agent must do positive work on the charge 9 Equipotentials Point B is at a lower potential than point A Points B and C are at the same potential The name equipotential surface is given to any surface consisting of a continuous distribution of points having the same electric potential r r VB - VA = V = - E ds = -E r = q0 V = -q0 E r = A = -E r cos = -Ed = VC - VA B VB = V C 10 Potential and Point Charges A positive point charge produces a field directed radially outward The potential difference between points A and B will be 1 1 VB - VA = keq - rB rA 11 Potential and Point Charges, cont The electric potential is independent of the path between points A and B It is customary to choose a reference potential of V = 0 at rA = Then the potential at some point r is q V = ke r 12 Electric Potential with Multiple Charges The electric potential due several to point charges is the sum of the potentials due to each individual charge This is another example of the superposition principle The sum is the algebraic sum qi V = ke i ri V = 0 at r = 13 Potential Energy of Multiple Charges Consider two charged particles The potential energy of the system is q1q2 U = ke r12 U = q1 V2 14 More About U of Multiple Charges If the two charges are the same sign, U is positive and work must be done to bring the charges together If the two charges have opposite signs, U is negative and work is done to keep the charges apart q1q2 U = ke r12 15 U with Multiple Charges, final If there are more than two charges, then find U for each pair of charges and add them Add them algebraically The total electric potential energy of a system of point charges is equal to the work required to bring the charges, one at a time, from an infinite separate to their final positions 16 Potential of a Charge Now remove one charge The potential due to charge q2 is U k e q2 V= = q1 r12 The equipotential surfaces for an isolated point charge are a family of spheres concentric with the charge 17 A spherical balloon contains a positively charged object at its center. (i) As the balloon is inflated to a greater volume while the charged object remains at the center, does the electric potential at the surface of the balloon 1. 2. 3. Increase Decrease Remain the same? 0% se cr ea 100% 0% re a sa R em ai n th e m e? se D ec In 18 A spherical balloon contains a positively charged object at its center. Does the electric flux through the surface of the balloon 1. 2. 3. Increase Decrease Remain the same? 0% se cr ea 100% 0% re a sa R em ai n th e m e? se D ec In 19 In Active Figure 20.6a, take q1 to be a negative source charge and q2 to be the test charge. (i) If q2 is initially positive and is replaced with a charge of the same magnitude but negative, does the potential at the position of q2 due to q1 1. 2. 3. increase, decrease remain the same? 10 20 In Active Figure 20.6a, take q1 to be a negative source charge and q2 to be the test charge. (ii) When q2 is changed from positive to negative, does the potential energy of the two-charge system 1. 2. 3. Increase Decrease Remain the same? 33% 33% 33% cr ea re a In ec R em ai n th e D sa m e? 10 21 se se Problem 20.12. Two point charges each of magnitude 2.00 C are located on the x axis. One is at x = 1.00 m and the other is at x = 1.00 m. (a) Determine the electric potential on the y axis at y = 0.500 m. (b) Calculate the change in electric potential energy of the system as a third charge of 3.00 C is brought from infinitely far away to a position on the y axis at y = 0.500 m. 22 Problem 20.18. Two particles, with charges of 20.0 nC and 20.0 nC, are placed at the points with coordinates (0, 4.00 cm) and (0, 4.00 cm) as shown in Figure P20.18. A particle with charge 10.0 nC is located at the origin. (a) Find the electric potential energy of the configuration of the three fixed charges. (b) A fourth particle, with a mass of 2.00 10 13 kg and a charge of 40.0 nC, is released from rest at the point (3.00 cm, 0). Find its speed after it has moved freely to a very large distance away. 23 Problem 20.68. Four balls, each with mass m, are connected by four nonconducting strings to form a square with side a as shown in Figure P20.68. The assembly is placed on a horizontal, nonconducting, frictionless surface. Balls 1 and 2 each have charge q, and balls 3 and 4 are uncharged. Find the maximum speed of balls 3 and 4 after the string connecting balls 1 and 2 is cut. 24

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