2009Chp29Soln - 29.20.Model:The electric potential between...

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29.20. Model: The electric potential between the plates of a parallel-plate capacitor is determined by the uniform electric field between the plates. Solve: (a) The potential difference across the plates of a capacitor is ( 29 ( 29 ( 29 ( 29 ( 29 9 3 C 4 2 12 2 2 0 0 0 0.708 10 C 1.00 10 m 200 V 4.00 10 m 8.85 10 C /N m Q A Qd V Ed d d A η ε - - - - × × = = = = = = ÷ × × (b) For d = 2.00 mm, V C = 400 V. Assess: Note that the units in part (a) are N m/C. But Exercise 29.17 showed that 1 N/C = 1 V/m, so 1 N m/C = 1 V. We also see that the potential difference across a parallel-plate capacitor is directly proportional to the plate separation. 29.38. Model: Mechanical energy is conserved. Visualize: Solve: Before the charges are released, the total mechanical energy is the potential energy of the three charges. ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 1 3 2 3 i 12 13 23 0 12 13 23 9 9 9 9 9 9 9 2 2 6 1 4 5.0 10 C 1.0 10 C 5.0 10 C 5.0 10 C 1.0 10 C 5.0 10 C 9.0 10 Nm /C 0.010 m 0.020 m 0.010 m 2.25 10 J q q q q q q E U U U r r r πε - - - - - - - = + + = + + × - × × × - × × = × + + = × After the charges are released and move very far (infinitely) apart, the total potential energy is zero. By the symmetry of the original configuration, the middle charge does not move when released, and the two 5.0 nC charges are moving at the same speed. The final energy is thus 2 2 2 2 6 f 1 1 2 2 3 3 1 i 6 2 3 1 1 1 1 2 2.25 10 J 2 2 2 2 2.25 10 J 4.7 10 m/s 4.7 cm/s 1.0 10 kg E m v m v m v m v E v - - - - = + + = = = × ÷ × ⇒ = = × = × 29.42. Model: Energy is conserved. The potential energy is determined by the electric potential. Visualize:
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This note was uploaded on 04/03/2012 for the course PHYSICS AN 101 taught by Professor N.a during the Spring '12 term at Clark College.

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2009Chp29Soln - 29.20.Model:The electric potential between...

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