d b a Low potential High potential − − − − − − − − − − − − − − − − + + + + + + + + + + + + + + + + E B High PE Low PE FIGURE 17–1 Work is done by the electric field in moving the positive charge from position a to position b. E B
When the electric force does positive work on a charge, the kinetic energy increases and the potential energy decreases. The difference in potential energy, is equal to the negative of the work, done by the electric field to move the charge from a to b; so the potential difference is (17 ; 2b) Note that electric potential, like electric field, does not depend on our test charge q . V depends on the other charges that create the field, not on the test charge q ; q acquires potential energy by being in the potential V due to the other charges. We can see from our definition that the positive plate in Fig. 17 – 1 is at a higher potential than the negative plate. Thus a positively charged object moves naturally from a high potential to a low potential. A negative charge does the reverse. The unit of electric potential, and of potential difference, is joules/coulomb and is given a special name, the volt , in honor of Alessandro Volta (1745 – 1827) who is best known for inventing the electric battery. The volt is abbreviated V, so Potential difference, since it is measured in volts, is often referred to as voltage . (Be careful not to confuse V for volts, with italic V for voltage.) If we wish to speak of the potential at some point a, we must be aware that depends on where the potential is chosen to be zero. The zero for electric potential in a given situation can be chosen arbitrarily, just as for potential energy, because only differences in potential energy can be measured. Often the ground, or a conductor connected directly to the ground (the Earth), is taken as zero potential, and other potentials are given with respect to ground. (Thus, a point where the voltage is 50 V is one where the difference of potential between it and ground is 50 V.) In other cases, as we shall see, we may choose the potential to be zero at an infinite distance. V a V a 1 V = 1 J C. V ba = V b - V a = pe b - pe a q = – W ba q . V ba W ba , pe b - pe a , SECTION 17 – 1 Electric Potential Energy and Potential Difference 475 C A U T I O N A negati v e charge has high PE w hen potential V is lo w b a Low potential V b High potential V a − − − − − + + + + + E B High PE for negative charge here FIGURE 17–2 Central part of Fig. 17 – 1, showing a negative point charge near the negative plate. Example 17 – 1. A negative charge. Suppose a negative charge, such as an electron, is placed near the negative plate in Fig. 17 – 1, at point b, shown here in Fig. 17 – 2. If the electron is free to move, will its electric potential energy increase or decrease? How will the electric potential change?
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- Spring '14