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Unformatted text preview: CHAPTER 19 ELECTRIC POTENTIAL ENERGY AND THE ELECTRIC POTENTIAL CONCEPTUAL QUESTIONS ____________________________________________________________________________________________ 1. REASONING AND SOLUTION The work done in moving a charge q from A to B is given by Equation 19.4: W q . For the cases in the drawing, we have AB A B ( V V = ) Case 1: AB (150 V 100 V) (50 V) W q q = = Case 2: AB [25 V (25 V)] (50 V) W q q = = Case 3: AB [10 V (60 V)] (50 V) W q q = = r The work done on the charge by the electric force is the same in each case. ___________________________________________________________________________________________ 2 . REASONING AND SOLUTION The potential at a point in space that is a distance r from a point charge q is given by Equation 19.6: V kq = / . When more than one point charge is present, the total potential at any location is the algebraic sum of the individual potentials created by each charge at that location. A positive point charge and a negative point charge have equal magnitudes. One of the charges is fixed to one corner of a square. If the other charge is placed opposite to the first charge along the diagonal of the square, then each charge will be the same distance L from the empty corners. The potential at each of the empty corners will be ( ) ( ) k Q k Q V L L + = + = q = +Q q = Q L L L L Therefore, if the potential at each empty corner is to be the same, then the charges must be placed at diagonally opposite corners as shown in the figure. ____________________________________________________________________________________________ 3 . REASONING AND SOLUTION The potential at a point in space that is a distance r from a point charge q is given by Equation 19.6: V = kq / r . When more than one point charge is present, the total potential at any location is the algebraic sum of the individual potentials created by each charge at that location. 982 ELECTRIC POTENTIAL ENERGY AND THE ELECTRIC POTENTIAL Three point charges have identical magnitudes, but two of the charges are positive and one is negative. These charges are fixed to the corners of a square, one to a corner, as shown in the figure. The potential at the empty corner is given by 3 1 2 2 q q q V L L L = + + L L q 3 q 1 q 2 L 2 Using q to denote the magnitude of each charge, we have the following possibilities: q 1 and q 2 are positive: 2 2 kq kq kq kq L L L L = + = V q 1 and q 3 are positive: 1 2 2 2 kq kq kq kq L L L L = + = V q 2 and q 3 are positive: 2 2 kq kq kq kq L L L L = + + = V In each case, the potential at the empty corner is positive. ____________________________________________________________________________________________ 4 . SSM REASONING AND SOLUTION Four point charges of equal magnitude are placed at the corners of a square as shown in the figure at the right....
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