Electrostatics Problems

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1 Name AP Physics B Electrostatics Problems Date Mrs. Kelly 1. How many excess electrons are contained in a charge of 30 C? 2. Calculate and compare the gravitational and electrostatic force between an electron and a proton separated by a distance of 1 x m. 3. Two charged balls are 20 cm apart. They are moved and the force between them is found to have been tripled. How far apart are they now? 4. What is the magnitude of the electrostatic force of attraction between an iron nucleus (q=+26e) and its innermost electron if the distance between them is 1.5 x m? 5. Three charged particles are arranged in a line as shown in the diagram below. What is the net electrostatic force on particle 3 due to the other two particles? 6. Particles of charge +70, +48, and 80 C are placed in a line as shown below. The center of one is 0.35 m from each of the others. Calculate the net force on the +70 C charge due to the other two. 7. Calculate the net electrostatic force on charge Q 2 due to charges Q 1 and Q 3 shown in the diagram below. 8. Four charges, each of +5 C, are placed at the corners of a square of 30 cm sides. Calculate the force on the charge located in the lower right corner of the square. 9. What is the magnitude and direction of the electrostatic force on an electron in a uniform electric field of strength 3500 N/C that points due east? 10. A proton is released in a uniform electric field and it experiences an electric force of 3.2 x N toward the south. What are the magnitude and direction of the electric field? 11. What is the magnitude of the acceleration experienced by an electron in an electric field of 600 N/C? 12. An electron is released from rest in a uniform electric field and accelerates to the north at a rate of 125 m/s 2. What is the magnitude and direction of the electric field? 13. A 1 x 10-9 kg spherical water drop that carries a charge of C is released from rest in an electric field of 125 V/m. What is the acceleration of the particle due to the electric field? 14. Calculate the magnitude and direction of the electric field at a point P which is 0.30 m to the right of a point charge Q = -3.0 x 10-6 C.

2 15. What is the magnitude and direction of the electric field at a point midway between a 8.0 C and a +6.0 C charge 4.0 cm apart? 16. Two point charges are separated by a distance of 0.10 m. One has a charge of 25 C and the other +50 C. a) What is the direction and magnitude of the electric field at a point P in between them, that is 0.02 m from the negative charge? b) If an electron is placed at rest at P, what will its acceleration (magnitude and direction) be? 17. The electric field midway between two equal but opposite point charges is 1750 N/C, and the distance between them is 0.16 m. What is the magnitude of the charge on each? 18. Determine the magnitude and direction of the electric field at the point P shown in the diagram below. The two charges are separated by a distance of 2a and the point P is a distance x out on the perpendicular bisector of the line adjoining them. Express your answers in terms of Q, x, a and k 19. Three charges, +3 C, -6 C and 9 C, are placed in order along a straight line with 20 cm between adjacent charges. Calculate the electric field at the following positions: a) Midway between the +3 C and 6 C charges. b) On the extension of the straight line and 20 cm beyond the 9 C charge. 20. Four charges, each of +5 C, are placed at the corners of a square of 30 cm sides. a) Calculate the electric field at the center of the square. b) Calculate the electric field at the center of one of the sides of the square. 21. How much work is done by the electric force in moving a 8.6 C charge from ground to a point whose potential is +75 V? 22. How much work is done by the electric force in moving a proton from a point with a potential of +100 V to a point where it is 50 V? Express your answer in both joules and electronvolts. 23. An electron gains 3.45 x J of kinetic energy when it is accelerated by an electric field in a computer monitor from plate A to plate B. What is the potential difference between the plates and which is at a higher potential? 24. A lightening flash transfers 4.0 C of charge and 4.2 MJ of energy to the Earth. Through what potential difference did the lightening travel? 25. How strong is the electric field between two parallel plates 5.2 mm apart if the potential difference between them is 220 V? 26. An electric field of 640 V/m is desired between two parallel plates 11.0 mm apart. How large a voltage should be applied? 27. What is the speed of a proton whose kinetic energy is 28.0 MeV? 28. What is the potential difference required to accelerate a proton from rest to a speed of 1 x 10 6 m/s? 29. How much kinetic energy will an electron gain if it falls through a potential difference of 21,000 V? 30. What potential difference is needed to give helium nucleus (q = 2e) 65.0 kev of kinetic energy?

3 31. What is the electric potential 15.0 cm from a 4.00 C point charge? 32. An electron starts from rest 72.5 cm from a fixed point charge with Q = C. How fast will the electron be moving when it is very far away? 33. Find the total electric potential due to the two point charges shown below at location A. 34. Find the total electric potential due to the two point charges shown below at location B. 35. Two point charges, Q 1 = nc and Q 2 = nc, are separated by 35.0 cm. a) What is the electric potential midway between the two charges? b) What is the potential energy of the pair of charges? 36. A point charge of 9.00 x 10-9 C is located at the origin. How much work is required to bring a positive charge of 3.00 x 10-9 C from infinity to the location x = 30.0 cm? 37. Three charges are situated at corners of a rectangle as shown in the diagram below. How much energy would be expended in moving the 8.0 C charge to infinity? 38. A +30 C charge is placed 32 cm from an identical +30 C charge. How much work would be required to move a C test charge from a point midway between them to a point 10 cm closer to either of the charges? 39. Consider point a which is 70 cm north of a 3.8 C point charge, and point b which is 80 cm west of the charge. Determine: a) The potential difference between points a and b (V b V a ) b) The difference in the electric field between points a and b (E b E a ) 40. The potential difference between two parallel wires in air is 120 V. They carry equal and opposite charge of magnitude 95 pc. What is the capacitance of the two wires? 41. How much charge flows from a 12.0 V battery when it is connected to a 9.00 F capacitor? 42. What is the capacitance of a pair of circular plates with radius of 5.0 cm separated by 3.2 mm of air? 43. An electric field of 8.50 x 10 5 V/m is desired between two parallel plates each of area 35.0 cm 2 and separated by 2.45 mm of air? What charge must be on each plate?

4 44. How strong is the electric field between the plates of a 0.80 F air-gap capacitor if they are 2.0 mm apart and each has a charge of 72 C? V is applied to a 7200 pf capacitor. How much energy is stored? 46. A homemade capacitor is assembled by placing two 9-inch pie plates 10 cm apart and connecting them to the opposite terminals of a 9 V battery. Estimate the following for the homemade capacitor: a) the capacitance b) the charge on each plates c) the electric field halfway between the plates d) the work done by the battery to charge the plates e) which of the above values change if a dielectric is inserted between the plates? 47. How does the energy stored in a capacitor change if a) the potential difference is doubled b) the charge on each plate is doubled c) the separation of the plates is doubled, as the capacitor remains connected to a battery 48. It takes 8.5 J of energy to move a 3.0 C charge from one plate of a 9.0 F capacitor to the other. How much charge is on each plate? 49. An uncharged capacitor is connected to a 24.0 V battery until it is fully charged, after which it is disconnected from the battery. A slab of paraffin ( =2.5) is then inserted between the plates. What will now by the voltage between the plates?

5 THE END!

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