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Unformatted text preview: On Chapter 19 Electric Potential Energy and the Electric Potential Conceptual Problems pp. 593: # 4, 6, 11 Problems pp. 594: # 8, 27, 29, 30, 36, 46, 54, 56, 66 ANSWERS TO FOCUS ON CONCEPTS QUESTIONS pp. 593: # 4, 6, 11 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. 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 ). 11. (c) The magnitude of the electric field between the plates is V E s = - (Equation 19.7). Since s is the same for all three capacitors, E is proportional to the potential difference q V = V right- V left between the right and left plates. V for capacitor C (300 V) is greater than that for capacitor B (250 V), which is greater than that for capacitor A (200 V). 1 Problems pp. 594: # 8, 27, 29, 30, 36, 46, 54, 56, 66 8. REASONING Let the electrons accelerate to point B from a condition of rest at point A . The speed v B of an electron at B is found from its kinetic energy 2 1 B B 2 KE mv = (Equation 6.2) at B . Because only the conservative electric and gravitational forces act on the electron, its total mechanical energy (the sum of its kinetic energy and potential energies) is conserved. Furthermore, if we assume that the electron only moves horizontally, then its gravitational potential energy mgh is constant during its acceleration, and we conclude that the sum of its kinetic energy KE B and electric potential energy EPE B at B is equal to the sum of its kinetic energy KE A and electric potential energy EPE A at A : 2 2 1 1 B B A A 2 2 EPE EPE mv mv + = + (1) The difference between the electric potential energy of the electron at B and at A , in turn, depends upon the charge q = e of the electron and the potential difference V B V A that it accelerates through:...
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