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習題六 25.41. (a) The potential on the x axis is 𝑉= 𝑞 2𝑞 1 − = 0 ⇔ 𝑥 = 𝑑, −𝑑 |𝑥| |𝑑 − 𝑥| 3 (b) The potential on the y axis is 𝑉= 𝑞 2𝑞 √3 − =0⇔𝑦=± 𝑑 |𝑦| √𝑑2 + 𝑦 2 3 (c) If the charge is positive the potential of each charge is always positive, so there is no point at zero potential except infinity E (r R/2) 0 E ( R/2 r R) E (r R) R3 r 2 radially outward 3 0 8r 7 R3 radially outward 24 0 r 2 25.45. (a) (b) Ex V 500 V 5.0 103 V/m (c) Here we treat the system as consisting of the parallel plates x 0.10 m and the electron. In that case U qV (1.60 1019 C)(500 V) 8.0 10 17 J. (d) Now we treat the electric field between the plates as being external, and we take the system to be the electron alone. In that V case the work done by the electric force is equal to W F E x qEx x q x x qV . Clearly the answer is the same in magnitude as the answer to (c). The only difference is that now we are discussing a positive external work being done on the system. W (1.60 1019 C)(500 V) 8.0 10 17 J. (e) Whether electrostatic potential energy is converted into kinetic energy, or external work speeds up the electron, either treatment tells us that the kinetic energy must be 8.0 1017 J. 25.59. We know Ex dV , so E B, and the electric field points in the x direction. dx