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Electrostatic Superposition Worksheet
Name:__________________ Date:_________________
1. Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in
Figure P15.10. (46.7 N left, 157 N right, 111 N left)
2. Three charges are arranged as shown in Figure P15.12. Find the magnitude and direction of the
electrostatic force on the 6.00 nC charge. (3.89X10-6 N, 11.30 below the x-axis)
Electrostatic Superposition Worksheet
Name:__________________ Date:_________________
3. Three point charges are located at the corners of an equilateral triangle as shown in the Figure (q = 2.00
µC, L = 0.950 m). Calculate the net electric force on the 7.00 µC charge. (0.242 N @ 300 below x-axis)
4. Three charges are at the corners of an equilateral triangle, as shown in the Figure. Calculate the electric
field at a point midway between the two charges on the x axis. (1880 N/C, 4.40below x-axis)
Electrostatic Superposition Worksheet
Name:__________________ Date:_________________
5. An object with a net charge of 29 µC is placed in a uniform electric field of 670 N/C, directed vertically.
What is the mass of the object if it "floats" in the electric field?( 0.00198 kg)
6. A small m = 2.00 g plastic ball is suspended by a L = 22.0 cm long string in a uniform electric field, as
shown in Figure P15.50. If the ball is in equilibrium when the string makes a 12.0° angle with the
vertical as indicated, what is the net charge on the ball? ( 4.17 µC )
Electrostatic Superposition Worksheet
Name:__________________ Date:_________________
7. Four point charges q= 4 mC are situated at the corners of a square with sides of length a= 2.0 m as in
Figure P15.4. Find the resultant force on the positive charge q.
Figure P15.4
8. Two small beads having positive charges 8 mC and 1 mC are fixed at the opposite ends of a horizontal
insulating rod, extending from the origin (the location of the larger charge) to the point d = 1m. As
shown in Figure P15.14, a third small charged bead is free to slide on the rod. At what position is the
third bead in equilibrium? (0.739 m)
Figure P15.14
Electrostatic Superposition Worksheet
Name:__________________ Date:_________________
9. Two small metallic spheres, each of mass 0.20 g, are suspended as pendulums by light strings from a
common point as shown in Figure P15.15. The spheres are given the same electric charge, and it is
found that they come to equilibrium when each string is at an angle of 5.0° with the vertical. If each
string is 30.0 cm long, what is the magnitude of the charge on each sphere? (7.22X10-9 C)
10. Two point charges lie along the y axis. A charge of q1 = -14.0 µC is at y = 8.0 m, and a charge of q2 = -7.0
µC is at y = -4.0 m. Locate the point (other than infinity) at which the total electric field is zero. (0.971
m)
Electrostatic Superposition Worksheet
Name:__________________ Date:_________________
11. Three charges are arranged as shown in the figure below. Find the magnitude and direction of the
electrostatic force on the charge at the origin. (1.38X10-5 N @ -1030 from + x-axis)
12. In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit around a proton.
The radius of the orbit is 5.3 10-11 m.
(a) Find the electrostatic force acting on each particle. (8.19X108 N)
(b) If this force causes the centripetal acceleration of the electron, what is the speed of the electron?
( 2.18X106 m/s)
Electrostatic Superposition Worksheet
Name:__________________ Date:_________________
13. An electron is accelerated by a constant electric field of magnitude 315 N/C.
(a) Find the acceleration of the electron.( 5.53X1013 m/s2)
(b) Use the equations of motion with constant acceleration to find the electron's speed after
1.15 10-8s, assuming it starts from rest.( 6.36X105 m/s)
14. A proton (m= 1.67X10-27 kg) accelerates from rest in a uniform electric field of 660 N/C. At some later
time, its speed is 1.40 106 m/s.
(a) Find the magnitude of the acceleration of the proton. (6.32X1010 m/s2)
(b) How long does it take the proton to reach this speed?(22.1X 10-6 s)
(c) How far has it moved in that interval?( 15.5 m)
(d) What is its kinetic energy at the later time?(1.64X10-15 J)
Electrostatic Superposition Worksheet
Name:__________________ Date:_________________
15. An electron is released a short distance above the surface of the Earth. A second electron
directly below it exerts an electrostatic force on the first electron just great enough to cancel the
gravitational force on it. How far below the first electron is the second? (5.08 m)
16. Each of the protons in a particle beam has a kinetic energy of 3.35 10-15 J. What are the
magnitude and direction of the electric field that will stop these protons in a distance of 1.50 m?
(14000 N/C, opposite the direction of the beam)
17. A 6.00 kg block carrying a charge Q = 45.0 µC is connected to a spring for which k = 100 N/m.
The block lies on a frictionless horizontal track, and the system is immersed in a uniform
electric field of magnitude E = 5.00 105 V/m, directed as shown in Figure P16.9. What is the
equilibrium position of the block? (0.225 m)
Electrostatic Superposition Worksheet
Name:__________________ Date:_________________
18. A 10 kg block that carries a charge of +2.5 mC is placed on a 370 incline, in a uniform electric
field parallel to the incline as shown in the figure below. The coefficient of friction between the
incline and the block is 0.22. If the block accelerates up the incline at the rate of 1.5 m/s2, draw
a free-body diagram for the block and find the electric field E. ( 33069 N/C )
E
300