Chapter 20 Practice Pr soln - pg Phys 299 Chapter 20...

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pg 1 Phys 299 Chapter 20 Practice Pr soln: #15, 16, 17, 22, 25, 27, 29,31, 35,38, 59, 60, 61,67 15: D EVELOP Since the magnitude of elementary charge e is 19 1.6 10 C, e - = × the number of electrons involved is given by / . Q e E VALUATE Substituting the values given in the problem statement, we find the number to be 20 19 25 C / 1.56 10 1.6 10 C N Q e - = = = × × 16.(a) The proton’s charge is 2 2 1 3 3 3 1 , e e e e = + - corresponding to a combination of uud quarks; (b) for neutron 0 = 2 1 1 3 3 3 - - corresponds to udd . 17. D EVELOP The gravitational force and the electrostatic force between a proton and an electron separated by a distance r are, respectively, grav 2 p e Gm m F r = and 2 elec 2 ke F r = E VALUATE The ratio of the two forces is 2 2 9 2 2 19 2 elec 2 11 2 2 27 31 grav 39 (9 10 N m /C )(1.6 10 C) (6.67 10 N m /kg )(1.67 10 kg)(9.11 10 kg) 2.3 10 p e F ke r F Gm m r - - - - × × = = × × × × Note that the spatial dependence of both forces is the same, and cancels out. A SSESS At all distances (for which the particles can be regarded as classical point charges), the Coulomb force is about 40 10 times stronger than the gravitational force. 22. The magnitude of the force is 2 9 2 2 19 2 10 2 2 2 18 2 (9 10 N m /C )(1.6 10 C) | | 7.74 10 N (0.41 0.36 ) 10 m p ke F r - - - × × = = = × + × r and its direction is from the proton (at 0) p r = r to the electron (at ˆ ˆ (0.41 0.36 ) nm), e r i j = + r for an attractive force, at an angle 1 tan (0.36/0.41) 41.3 θ - = = ° to the x axis. 25. D EVELOP Equation 20.2a shows that the electric field strength (magnitude of the field) at a point is equal to the force per unit charge that would be experienced by a charge at that point: E = F / q E VALUATE (a) With 68 nC, q = we find the field strength to be 6 150 mN 2.21 10 N/C | | 68 nC F E e = = = × (b) The force experienced by another charge, 35 C, q μ ′ = in the same field is 6 (35 C)(2.21 10 N/C) 77.2 N F q E μ = = × = 27. D EVELOP The electric field strength at a distance r from a point source charge q is given by Equation 20.3: 2 ˆ kq E r r = r . The proton in a hydrogen atom behaves like a point charge. E VALUATE At a distance of one Bohr radius ( a 0 = 0.0529 nm) away, the electric field strength is
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pg 2 9 2 2 19 11 2 11 2 0 (9 10 N m /C )(1.6 10 C) 5.15 10 N/C (5.29 10 m) ke E a - - × × = = = × × 29. As shown in Equation 20.5, the electric dipole moment p is the product of the charge q
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