Capitulo 23 de mate 3

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?
[pic]; 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?
[pic]; F = 750 N, attraction

23-3. An alpha particle consists of two protons (qe =1.6 x 10-19 C) and two neutrons (no charge). What is the repulsive force between two alpha particles separated by 2 nm?
qα = 2(1.6 x 10-19 C) = 3.2 x 10-19 C
[pic]; 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?
[pic]; F = 8.52 x 10-8 N
23-5.What is the separation of two -4 (C charges if the force of repulsion between them is 200 N?
[pic]; 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?
[pic]; 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 placedin contact for a few moments and then separated again by 40 mm. What is the new force? Is it attractive or repulsive?
[pic]; 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.
[pic] [pic];
F =5.62 N, repulsion

*23-8. Two point charges initially attract 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?
[pic]; r1 = 3 r2
[pic] 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 (Ccharge placed midway between the two charges?
[pic]
F13 = 2.10 x 104 N, directed to the left
[pic]; 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 thirdcharge of +10 (C located at the midpoint?
[pic]
F13 = 2025 N, directed to the right
[pic]; 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?
[pic][pic];
Both to right, so FR = F13 + F23 = 1080 N + 5940 N; F = 7020 N, rightward.
23-12. A +6 (C charge is 44 mm to 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?
[pic]
[pic];
Both to right, so FR = F13 + F23 = 360 N + 187.5 N; F = 548 N, rightward

*23-13. A64-(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 below the 16 (C charge?
[pic]
[pic]
[pic]
F13 = 2033 N, 59.00 N of W
[pic]= 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
[pic]; ( = 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 above a -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?
[pic]
[pic]
[pic]
F13 = 2564 N, 60.640 N...