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Unformatted text preview: 25 CHAPTER OUTLINE 25.1 Potential Difference and Electric Potential 25.2 Potential Difference in a Uniform Electric Field 25.3 Electric Potential and Potential Energy Due to Point Charges 25.4 Obtaining the Value of the Electric Field from the Electric Potential 25.5 Electric Potential Due to Continuous Charge 25.6 Electric Potential Due to a Distributions Charged Conductor 25.7 The Milliken Oil Drop Experiment 25.8 Application of Electrostatistics Electric Potential ANSWERS TO QUESTIONS Q25.1 When one object B with electric charge is immersed in the electric field of another charge or charges A , the system possesses electric potential energy. The energy can be measured by seeing how much work the field does on the charge B as it moves to a reference location. We choose not to visualize A s effect on B as an action-at-a-distance, but as the result of a two- step process: Charge A creates electric potential throughout the surrounding space. Then the potential acts on B to inject the system with energy. Q25.2 The potential energy increases. When an outside agent makes it move in the direction of the field, the charge moves to a region of lower electric potential. Then the product of its negative charge with a lower number of volts gives a higher number of joules. Keep in mind that a negative charge feels an electric force in the opposite direction to the field, while the potential is the work done on the charge to move it in a field per unit charge. Q25.3 To move like charges together from an infinite separation, at which the potential energy of the system of two charges is zero, requires work to be done on the system by an outside agent. Hence energy is stored, and potential energy is positive. As charges with opposite signs move together from an infinite separation, energy is released, and the potential energy of the set of charges becomes negative. Q25.4 The charge can be moved along any path parallel to the y-z plane, namely perpendicular to the field. Q25.5 The electric field always points in the direction of the greatest change in electric potential. This is implied by the relationships E V x x = , E V y y = and E V z z = . Q25.6 (a) The equipotential surfaces are nesting coaxial cylinders around an infinite line of charge. (b) The equipotential surfaces are nesting concentric spheres around a uniformly charged sphere. Q25.7 If there were a potential difference between two points on the conductor, the free electrons in the conductor would move until the potential difference disappears. 51 52 Electric Potential Q25.8 No. The uniformly charged sphere, whether hollow or solid metal, is an equipotential volume. Since there is no electric field, this means that there is no change in electrical potential. The potential at every point inside is the same as the value of the potential at the surface....
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