ELECTROSTATICS PROBLEMS

Electrostatics Problems

PROBLEMS #43 TO #50 CHANGED OR ADDED AS OF 6-23-01. ANSWERS/SOLUTIONS MUST STILL BE PROVIDED

This page has a new "Online Sources of Additional Problems" written below.

1. A test charge of 0.01 micro-coulombs is placed in an electric field, the intensity of which is 10⁶ v/m. What force acts on the charge?

2. A charge of + 5.12 x 10^-3 micro-coulombs is located 16 cm from point “A”. What is the magnitude and direction of the electric field intensity at point “A”?

3. What would be the magnitude of the electric field intensity at a distance of 5 cm from a charge of - 2 x 10^-3 micro-coulombs?

4. Two charges of + 8 x 10^-4 and - 4 x 10^-4 micro-coulombs are 12 cm apart. What is the magnitude of the electric field intensity at a point mid-way between the two charges, at a point 4 cm to the right of the first charge?

5. Two charges of + 1,000 and - 1,250 micro-micro-coulombs are 20 cm apart. What is the magnitude of the electric field intensity at a point 5 cm from the second charge and on a line prolonged which connects them?

6. At what distance from a small sphere possessing a charge of 10 micro-coulombs would the electric field intensity of 100 v/m?

7. If the electric field has an intensity of 450 v/cm, what would be the force in newtons on a charge of 1.5 micro-coulombs?

8. What is the effective field intensity if a force of 10 newtons is exerted on a charge of 5 micro-coulombs?

9. If a charge of 60 micro-coulombs is moved from a point in space where the potential is - 10 volts to a point where it is + 30 volts. How much work, in joules, is required?

10. Two positive charges of 6 x 10^-6 coulombs are separated by 0.5 m. What force exists between the charges?

11. A negative charge of 2 x 10^-4 coulombs, and a negative charge of 8 x 10^-4 coulombs are separated by 0.3 m. What force exists between the two charges?

12. What is the mutual electrostatic force between a positive charge of 0.0008 coul. and a negative charge of 0.0003 coul. that are separated by 0.7 m?

13. Determine the force between two positive charges of 1 coul. each which are separated by 1 m?

14. A negative charge of 6 x 10^-6 coulombs exerts an attractive force of 64.8 nt on a second charge 0.05 m away. What is the value of the second charge?

15. A positive charge of 2 x 10^-6 coulombs is 0.06 m from a second positive charge of 4 x 10^-6 coulombs. What force exists between the two charges?

16. The two objects in problem #15 each have a mass of 5 grams and are free to move in a frictionless medium. What instantaneous acceleration will the two objects experience when they are released?

17. Three neutral pith balls are arranged in a straight line. A charged bakelite rod is brought near each end. The pith balls are separated while the rods are in place. What charge will each pith ball have? Why?

18. A 1 x 10^-5 kg pith ball carries a + 0.40 micro-coulomb charge. The pith ball is suspended in an electric field on the end of a fine 25 cm length of thread. The electric field is horizontal and deflects the ball 1.5 cm to one side of a vertical line through its point of suspension.

(A) What is the force on the pith ball?

(B) What is the value of the electric field?

19. A 10 g mass carries a charge of + 2 coulombs and is located at a point where the electric field is 50 v/m. What force acts on this mass?

20. A 2 kg mass carries a charge of + 0.01 coul. and is located where the electric field is 3 v/m. What is its acceleration?

21. What is the acceleration of a proton in an electric field of 10³ v/m?

22. At a point 1 x 10^-8 cm from an electron, determine the:

(A) electric field

(B) electric potential.

23. A charge of + 5 coul. is 1 m away from a charge of - 9 coul. At the midpoint of the line between the two charges, find the:

(A) electric field

(B) electric potential.

24. Find the electric potential at the geometric center of the following diagram.

25. What is the potential energy of an electron located at a point where the electric potential is 1,000 v?

26. Two points “A” and “B” are on the same electric field line. The distance between them is 5 x 10^-4 m. The potential at “A” is 5.123 v and the potential at “B” is 5.158 v. What is the magnitude and direction of the electric field from point “B” to “A”?

27. What is the value of the vertical electric field that can support the weight of an electron?

28. A 3 gram mass (q₂) carries a charge of + 5 coul. and is placed a certain distance from another charged mass (q₁), which creates a uniform electric field. If q₂ starts from rest at its initial position and 2 seconds later has traveled a distance of 10 cm, calculate the magnitude of the electric field at its original position.

29. An electron is initially at rest in a uniform electric field of 2.5 v/m. What will be the velocity of the electron 10^-9 seconds later?

30. A proton has an initial velocity of 10⁸ cm/s in exactly the opposite direction to a uniform electric field of 0.2 v/m. How far will the proton travel before coming to rest?

31. Three charges, each one + 7 coulombs are placed at three corners of a square (positons A, B, and C) whose sides are 3 cm in length.

(A) What is the electric field at the unoccupied corner?

(B) What is the electric potential (phi sub D) at the unoccupied corner ?

(C) What is the difference in electric potential between the unoccupied corner and a point at the very center of the square (position E)?

32. Charges of + 3 coul. and - 4 coul. are placed on opposite ends of the diagonal of a square 1.5 cm on each edge.

(A) What is the potential difference between the two unoccupied corners?

(B) What is the potential difference between the center and one of the unoccupied corners?

33. Two charges of + 3.5 coul. each are in a straight line with each other and are separated by a distance of 2.5 cm. Where may we place a third charge of - 4 coul. where the net force acting on it will be zero?

34. A 4.5 x 10^-3 kg sphere is hanging on a string 2.0 m in long between two oppositely charged parallel plates. At equilibrium, the ball is pulled 2 cm from its original position.

(A) What is the value of the electric force on the sphere? [The electric force on each elementary charge between the plates is 3 x 10^-14 nt.]

(B) What is the number of excess electric particles on the sphere?

35. Two points differ in potential by 75,000 volts. How much work is required to carry 2 x 10^-9 coulombs from the point of lower to the point of higher potential?

36. The uniform electric field between two parallel plates has an intensity of 7,000 nt/coul. How much work would be required to carry a charge of + 5 micro-coulombs from the negative to the positive plate if the plates are separated 4 cm?

37. A charge of 0.52 micro-coulombs is placed in an electric field whose intensity is 4.5 x 10⁵ newtons/coulomb. What is the magnitude of the force acting on the charge?

38. A sphere of mass 1.5 milligram possesses a charge of 39 micro-coulombs. What is the electric field at a point 15 cm from that sphere?

39. A small sphere is given a charge of 20 micro-coulombs and a second sphere of equal diameter located 10 cm away is given a charge of -5 micro-coulombs. What is the force acting between the two spheres?

40. Two pith balls are placed 30 cm apart and are charged equally to repel each other with a force of 120 nt. Compute the charge on each ball.

41. A sphere having a positive charge of 30 microcoulomb and a second sphere having a positive charge of 50 microcoulomb are separated by 6 meters. Determine the COMBINED ELECTRIC FIELD INTENSITY between them at point "A", which is located 2 meters to the right of the first sphere and 4 meters to the left of the second sphere. Include the net field's direction.

42. Using the sphere setup in problem #41 above, where may a body be placed having a NEGATIVE charge of (-) 3.5 coulombs so that the net force acting on it will be zero?

43. Three charged bodies are placed at the corners of a square 4 meters on each edge as follows: A negative charge of 6 microcoulombs is placed in the upper left corner "A", a postive charge of 8 microcoulombs is placed in the upper right corner "B", and a negative charge of 4 microcoulombs is placed in the lower right corner "C".

(A) Determine the difference in electric potential between the lower left unoccupied corner (point D) and the center of the square (point E).

(B) Determine the amount of work required to move a charge of (-) 4 microcoulombs between point E and point D.

(C) What will be the instantaneous acceleration of a (+) 6 microcoulomb charge located at point D when it is released? In what direction will this charge move? How long will it take to travel to point E or an equal distance away from from point D, assuming the acceleration does not change?

44. A mass of electrons having a charge of (-) 2 microcoulombs is placed 2.45 m from a body having a positive charge of 5 microcoulombs.

(A) Find the electric field intensity at the location of the electrons due to the presence of the charged body.

(B) Find the mutual electrostatic potential energy (cap phi).

(C) If the mass of electrons is originally held at rest, determine the instantaneous acceleration of the mass when released.

45. An electron is placed in the electric field of a charged body where the intensity of the field is 4.5 x 10⁵nt/c.

(A) What is the magnitude of the electromagnetic force acting on the electron?

(B) What will be the acceleration of the electron as it moves through the electric field once it is set free? (m_e = 9.11 x 10^-31 kg)

46. A charged body "B" of 5 microcoulombs is placed in the electric field of another charged body "A", where the force of repulsion between them is 1.5 x 10^-4 newtons.

(A) What is the intensity of the electric field at that location?

(B) By what distance are these two charged bodies separated if the charge on the body "B" is 5 x 10^-3 coulombs?

47. You carefully place an electron 1 centimeter from a proton.

(A) What is the potential energy of the electron at that location?

(B) What is the electric potential of the proton at that location?

48. A charged metal sphere of 5 microcoulombs is placed in the electric field of a Van De Graff generator having a charge of 2 x 10^-6 coulombs. The electric field of the generator at that location has an intensity of 1.8 volts/meter.

(A) What force is exerted on the sphere?

(B) How far from the generator is the sphere?

49. A (+)6 microcoulomb charge is placed 12 meters to the left of a (+)8 microcoulomb charge.

(A) Determine the combined field intensity at a point "X", 7 meters to the right of the (+)8 microcoulomb charge.

(B) Determine the combined electric potential at point X.

(D) Determine the force acting between the charges in this system.

(E) Where may we place a charge of +6.8 coulombs so that the net force acting on it will be as small as possible?

(F) Determine the electric field intensity at the point determined in part (E).

50. Determine the magnitude of the electric field required to support five protons. Also determine the electric force required to support these protons.

Online Sources of Additional Problems:

Prentice-Hall Publishers, "Physics for Scientists and Engineers, 3d edition": Chapter 21 - Electric Charge and Electric Field. Click on "Physlet Problems" in the left text window. Solve Physlet problem #3 (similar to problems #33 and #42 above). Solve Physlet problem #4 - read the hint (similar to Self-Test problem #22 below). Solve Physlet problem #6 - checks your understanding of a "test" charge. Solve Physlet Problem #7 (a variation of problems #2, #3, #6 above). Solve Physlet problems #8 and #9 - check your understanding of "lines of force". Check your accuracy by clicking on the "Submit For Grading" button at the bottom of the page. Next, go to the left text window and click on "Practice Problems". Solve as many as you can, and submit to have your answers graded.

Univ. of Winnipeg

Univ. of Boston Review all problems having to do with electric fields and electric potential found in the listed exercises for Test 1.

Univ. of Hawaii (SureMath) - Index for Electricity & Magnetism: Scroll down the page to the set of problems. Solve the first five problems, using the solution link as a check. Next scroll to the top of this page, and click on the "To: Physics Problems" button". Click on the link titled "More Physics Problems" as part of The Journal of Modern Problem Solving. Under the "Physics" section titled "Electrostatics", solve "The number of electrons in a given amount of charge". Also, solve "Force on a charge due to two other charges", using our "addition of force vector components" method learned during the study of vectors. Study the method they use to solve this problem.

Univ. of Oregon Click on "Electricity and Magnetism". Solve the two problems shown, then check your work with the linked solutions.

Self-Test

Multiple Choice:

1. When a glass rod is rubbed with a piece of silk, the charge on the rod is:

(A) negative (C) positive

(B) either positive or negative (D) unchanged

2. A negatively charged brass ball “A” is brought near an insulated brass ball “B” and then removed. Ball “B” now has:

(A) a negative charge

(B) no charge

3. Charge density:

(A) can be measured in volts/m (C) is greatest at the point of least curvature

(B) is least at the point of a lightning rod (D) is greatest at the point of greatest curvature

4. Equipotential lines:

(A) terminate normal to the surface of a charged body

(B) are normal to the electric lines of force

(D) originate normal to the surface of a charged body

5. When a rubber rod is rubbed with fur, the rubber rod acquires a positive charge:

(A) true

(B) false

6. The practical unit of potential difference is the:

(A) coulomb (C) volt

(B) farad (D) joule

7. When an isolated hollow conductor is charged, the electric charge resides:

(A) on the outside surface (C) equally distributed between the inside and the outside surface

(B) on the inside surface (D) at the geometrical center of the conductor

8. The coulomb is a unit of:

(A) force (C) charge

(B) capacitance (D)potential

9. A device used for the detection of an electric charge is a(n):

(A) proof plane (C) leyden jar

(B) electrophorus (D) electroscope

10. A negatively charged body is held near the knob of a neutral electroscope. The leaves of the electroscope diverge. When the charged body is removed, the electroscope is:

(A) uncharged (C) positively charged

(B) either positively or negatively charged (D) negatively charged

11. An insulator is a material that:

(A) has more protons than electrons; (C) has more electrons than protons;

(B) allows electrons to pass freely; (D) allows electrons to pass with difficulty.

12. Of the following terms, ALL refer to electrostatic generators EXCEPT:

(A) Van deGraff (C) Whimshurst

(B) coulomb (D) electrophorus

13. An electric charge is produced on a neutral body “A” when touched by a charged body “B”. Body “A” is said to be charged:

(A) by induction (C) by conduction

(B) positive (D) negative

14. Two bodies “A” and “B” have equal masses. Body “A” acquires a negative charge and body “B” acquires a positive charge. The mass of “A” is now:

(A) less than “B”

(B) greater than “B”

15. The leaves of a negatively charged electroscope diverge when an electrified body was brought near it. The electrified must have been:

(A) a conductor (C) an insulator

(B) negatively charged (D) positively charged

16. A bakelite rod is mounted so that it can swing freely. When a glass rod is brought near to it, the rods attract each other. This action indicates that:

(A) the glass is positively charged (C) the bakelite rod is negatively charged

(B) the rods are oppositely charged (D) one of the two rods is charged

17. When a positively charged cloud passes over a tree, the tree becomes charged negatively by:

(A) induction (C) electrolysis

(B) conduction (D) contact

18. Referring to question #5, whenever the charge on the bakelite rod, the charge on the fur would be of the:

(A) same charge and equal in amount (C) same charge and unequal in amount

(B) opposite charge and equal in amount (D)opposite charge and unequal in amount.

19. An electric charge can be retained on a metal rod if the rod has previously been:

(A) grounded (C) polished

(B) heated (D) insulated

20. If a neutral body becomes positively charged electrically, we know that it has:

(A) lost electrons (C) lost protons

(B) gained electrons (D) gained protons

21. When you touch a negatively charged object, electrons:

(A) will flow from you to the object

(B) may flow either way

22. If the distance between two isolated electric charges changes from 10 cm to 5 cm, the force between them is now:

(A) four times as great (C) one-half as great

(B) one-fourth as great (D) twice as great

23. The free electron, according to modern atomic theory:

(A) has the same charge as the proton

(B) has slightly less mass then the proton

(D) determines the property of a solid as an electric conductor

24. A negatively charged body is held near the knob of a negatively charged electroscope. The leaves of the electroscope:

(A) diverge (C) remain unchanged

(B) collapse (D) collapse and then diverge

25. The number of lines of force per unit area normal to an electric field is a measure of its:

(A) potential gradient (C) field intensity

(B) potential difference (D) repulsive force

26. The lines of force of an electric field:

(A) cross each other at regular intervals

(B) cross each other irregularly

27. The distance that the leaves of an electroscope stand apart is an indication of:

(A) the sign of the charge

(B) the potential of the charge

28. When a bakelite rod is rubbed with fur, the fur acquires a positive charge:

(A) true

(B) false

29. A substance along which electrons are not free to move is known as a(n) ________.

30. If a neutral body becomes positively charged electrically, we know that it has:

(A) gained electrons (C) gained protons

(B) lost electrons (D) lost protons

31. The nucleus of an atom:

(A) always has a positive electric charge

(B) is electrically neutral

(D) may be either positively or negatively charged or neutral

32. An electron enters the space between a pair of parallel oppositely charged plates at a high velocity along a path initially parallel to the plates. As long as it is between the plates, the electron will experience a force directed:

(A) toward the positive plate (C) parallel to the plates

(B) toward the negative plate (D) always perpendicular to its instantaneous velocity

33. As the distance between a pair of metal plates maintained at a constant difference of potential

increases, the electric field intensity:

(A) increases

(B) decreases

34. The work needed to move an electric charge between two points is measured in:

(A) statcoulombs (C) ergs

(B) statvolts (D) statvolts/meter

35. As the electric field intensity at a point increases, the force per unit charge:

(A) increases

(B) decreases

36. A test charge is placed near a charged metal object. If the distance between the test charge and the charged object is tripled, the force on the test charge will be multiplied by:

(A) 1/9 (C) 3

(B) 1/3 (D) 9

37. The electric field intensity is at a maximum at the midpoint between:

(A) two similar charges (C) a neutral charge and either a positive or negative charge

(B) two dissimilar charges (D) none of the above.

38. The electric force per unit charge is known as:

(A) electric potential

(B) electric field

39. If charges equal in magnitude but opposite in sign are placed diagonally in opposite corners of a square, the electric field intensity will be at:

(A) a maximum

(B) a minimu

40. The electric potential in question #39 will be:

(A) at a maximum

(B) at a minimum

41. If three charges equal in magnitude and of the same sign are place at three of the four corners of a square, how will they interact with an electron at the unoccupied corner as opposed to the center of the square:

(A) a larger force

(B) a smaller force

42.An aluminum disk is charged using a bakelite electrophorus plate rubbed with flannel. The disk is brought NEAR a leaf electroscope charged by conduction using a charged bakelite rod.

(A) The positively charged disk will cause the negatively charged leaves to repel even further as a greater negative charge is induced on them.

(B) The positively charged disk will cause the negatively charged leaves to move slightly closer together as electrons are drawn upward toward the ball on the electroscope.

(C) The negatively charged disk will cause the negatively charged leaves to repel even further as a greater negative charge is induced on them.

(D) The negatively charged disk will cause the positively charged leaves to move slightly closer together as free electrons on the electroscope are repelled downward onto the leaves.

(E) None of the choices above.

43. A charged bakelite rod is placed NEAR the ball of a neutral leaf electroscope, which causes the leaves to separate. The electroscope is then charged by permanent induction while the rod remains nearby.

(A) The original charge on the leaves was negative, but becomes positive following permanent induction.

(B) The original charge on the leaves was negative, and remains negative following permanent induction.

(D) The original charge on the leaves was positive, and remains positive following permanent induction.

44. A Faraday Ice Pail is charged by conduction with the charged aluminum disk of a lucite electrophorus rubbed with silk. A negatively charged pith ball is suspended within the cavity of the pail.

(A) Electrons are transfered from the disk to the pail, giving the pail a net negative charge. The negatively charged pith ball, however, remains unaffected within the pail.

(B) The negative charge on the inner surface of the pail repels the negatively charged pith ball, making it impossible for it to remain within the pail.

(C) Electrons are transfered from the pail to the positively charged disk, giving the pail a net positive charge. The negatively charged pith ball will be attracted to the positive charge on the inner surface of the pail.

(D) The positive charge on the inner surface of the pail has no affect on the negatively charged pith ball.as it is placed within the pail.

45. Two neutral induction spheres are placed in contact with one another as a charged aluminum disk from a bakelite electrophorus rubbed with flannel is placed NEAR the left sphere. While the disk is held in place, the spheres are separated. A pith ball, previously touched with the disk, is brought close to the right sphere.

(A) The positively charged pith ball will repel from the positive charge on the right sphere.

(B) The positively charged pith ball will be attracted to the negative chare on the right sphere.

(D) The negatively charged pith ball will be attracted to the positive charge on the right sphere.