# Chapter 23. the electric force

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Chapter 23. The Electric Force

Coulomb's Law
23-1. Two balls each having a charge of 3 C are separated by 20 mm. What is the force of repulsion between them?
; F = 202 N

23-2. Two point charges of -3 and +4 C are 12 mm apart in a vacuum. What is the electrostatic force between them?
; F = 750 N, attraction

23-3. An alpha particle consists of two protons (qe = 1.6 x10-19 C) and two neutrons (no charge). What is the repulsive force between two alpha particles separated by 2 nm?
q = 2(1.6 x 10-19 C) = 3.2 x 10-19 C
; F = 2.30 x 10-10 N
23-4. Assume that the radius of the electron's orbit around the proton in a hydrogen atom is approximately 5.2 x 10-11 m. What is the electrostatic force of attraction?
; F = 8.52 x 10-8 N
23-5. What is theseparation of two -4 C charges if the force of repulsion between them is 200 N?
; r = 26.8 mm
23-6. Two identical charges separated by 30 mm experience a repulsive force of 980 N. What is the magnitude of each charge?
; q = 9.90 C

*23-7. A 10 C charge and a -6 C charge are separated by 40 mm. What is the force between them. The spheres are placed in contact for a fewmoments and then separated again by 40 mm. What is the new force? Is it attractive or repulsive?
; F = 338 N, attraction
When spheres touch, 6 C of charge are neutralized,
leaving 4 C to be shared by two spheres, or
+2 C on each sphere. Now they are again separated.
;
F = 5.62 N, repulsion

*23-8. Two point charges initiallyattract each other with a force of 600 N. If their separation is reduced to one-third of its original distance, what is the new force of attraction?
; r1 = 3 r2
F2 = 5400 N

The Resultant Electrostatic Force
23-9. A +60 C charge is placed 60 mm to the left of a +20 C charge. What is the resultant force on a -35 C charge placed midway between the two charges?F13 = 2.10 x 104 N, directed to the left
; F13 = 2.10 x 104 N, directed to right.
FR ¬= F13 + F23 = (-2.10 x 104 N) + (0.700 x 104 N); FR = -1.40 x 104 N, left.

23-10. A point charge of +36 C is placed 80 mm to the left of a second point charge of -22 C. What force is exerted on third charge of +10 C located at the midpoint?

F13 = 2025 N, directed to the right; F13 = 1238 N, directed to right.
FR ¬= F13 + F23 = 2025 N + 1238 N; FR = 3260 N, left.
23-11. For Problem 23-10, what is the resultant force on a third charge of +12 C placed between the other charges and located 60 mm from the +36 C charge?

;
Both to right, so FR = F13 + F23 = 1080 N + 5940 N; F = 7020 N, rightward.
23-12. A +6 C charge is 44 mmto the right of a -8 C charge. What is the resultant force on a -2 C charge that is 20 mm to the right of the -8 C charge?

;
Both to right, so FR = F13 + F23 = 360 N + 187.5 N; F = 548 N, rightward

*23-13. A 64-C charge is locate 30 cm to the left of a 16-C charge. What is the resultant force on a -12 C charge positioned exactly 50 mm belowthe 16 C charge?

F13 = 2033 N, 59.00 N of W
= 691 N, upward.
Fx = 0 – F13 cos 59.00 = -(2033 N) cos 590 ; Fx = -1047 N
Fy = F23 + F13 sin 59.00 = 691 N + (2033 N) sin 590; Fy = 2434 N
;  = 66.70 N of W.
Resultant force: FR = 2650 N, 66.70 N of W (or 113.30)

*23-14. A charge of +60 nC is located 80 mm abovea -40-nC charge. What is the resultant force on a -50-nC charge located 45 mm horizontally to the right of the -40-nC charge?

F13 = 2564 N, 60.640 N of W
= 8889 N, rightward.
Fx = – F13 cos 60.640 + F23 = - (2564 N) cos 60.640 + 8889 N ; Fx = 7632 N
Fy = +F13 sin 60.640 + 0 = (2564 N) sin 60.640 ; Fy = 2235 N
; FR =...

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