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Unformatted text preview: CHAPTER 19 ELECTRIC POTENTIAL ENERGY AND THE ELECTRIC POTENTIAL ANSWERS TO FOCUS ON CONCEPTS QUESTIONS ____________________________________________________________________________________________ 1. (d) The force on the positive charge is in the same direction as the electric field, and the displacement of the charge is opposite to the direction of the force. Therefore, the work is negative (see Section 6.1). The electric potential energy at point B differs from that at A by EPE B- EPE A = - W AB (Equation 19.1). Since W AB is negative, EPE B is greater than EPE A . 2. (d) The electric potential energy EPE is related to the electric potential V by EPE = q V (Equation 19.3). So, even though the electric potentials at two locations are the same, the electric potential energies are different since the charges placed at these locations are different. 3. V B- V A = 2 10 V -5.0 4. (a) The change in the protons electric potential energy (EPE B- EPE A ) in going from A to B is related to the change in the potential ( V B- V A ) by Equation 19.4 as EPE B- EPE A = (+ e ) ( V B- V A ), where + e is the charge on the proton. On the other hand, the change in the electrons electric potential energy (EPE A- EPE B ) in going from B to A is related to the change in the potential ( V A- V B ) by EPE A- EPE B = (- e )( V A- V B ), where - e is the charge on the electron. Comparing the right-hand sides of these two equations shows that the change in the protons electric potential energy is the same as the change in the electrons electric potential energy. 5. (c) According to Equation 19.6, the potential produced by the charge q is V = kq / r . The smaller the value of r , the greater is the potential. The potential, however, does not depend on the charge ( q or 2 q ) placed at points P 1 or P 2 . See Section 19.3. 6. (e) The total electric potential at the origin is the algebraic sum of the potentials due to all the charges. Since each potential is of the form V = kq / r (Equation 19.6) and r is same for each charge, the total electric potential is proportional to the sum of the charges. The sum of the charges in A (+4 q ) equals the sum in C (+4 q ), which is greater than the sum in B (+2 q ). 7. (b) The electric potential energy of the two charges in the top drawing is EPE = q V , where V = k q / r is the electric potential produced by the charge at the origin (see Equation 19.6). 238 ELECTRIC POTENTIAL ENERGY AND THE ELECTRIC POTENTIAL Thus, EPE = k qq / r . In a similar fashion, the electric potential energy for the charges in the bottom drawing is k q (2 q )/(2 r ) = k qq / r , which is the same as that in the top drawing. 8. V B- V A = 3 6.7 10 V 9. (a) The electric potential energy EPE of two charges q 1 and q 2 is EPE = kq 1 q 2 / r , where r is the distance between them (see Section 19.3). Since the distance r is the same for all four pairs of charges, the electric potential energy is proportional to the product q 1 q 2 of the charges. The products of the charges in A and C are the same (+12charges....
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