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Electric Charge and Electric Field

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  1. Electric Charge and Electric Field

  2. Static Electricity; Electric Charge and Its Conservation • Electric Charge in the Atom • Insulators and Conductors • Induced Charge; the Electroscope • Coulomb’s Law • The Electric Field • Electric Field Calculations for Continuous Charge Distributions

  3. Field Lines • Electric Fields and Conductors • Motion of a Charged Particle in an Electric Field • Electric Dipoles • Electric Forces in Molecular Biology: DNA • Photocopy Machines and Computer Printers Use Electrostatics

  4. Electric Charge and Its Conservation Charge comes in two types, positive and negative; like charges repel and opposite charges attract.

  5. Electric Charge and Its Conservation Electric charge is conserved – the arithmetic sum of the total charge cannot change in any interaction.

  6. Electric Charge in the Atom Atom: Nucleus (small, massive, positive charge) Electron cloud (large, very low density, negative charge)

  7. Electric Charge in the Atom Polar molecule: neutral overall, but charge not evenly distributed

  8. Insulators and Conductors Conductor: Charge flows freely Metals Insulator: Almost no charge flows Most other materials Some materials are semiconductors.

  9. Induced Charge Metal objects can be charged by conduction:

  10. Induced Charge They can also be charged by induction, either while connected to ground or not:

  11. Induced Charge Nonconductors won’t become charged by conduction or induction, but will experience charge separation:

  12. the Electroscope The electroscope can be used for detecting charge.

  13. Electric Charge I 1)one is positive, the other is negative 2) both are positive 3) both are negative 4) both are positive or both are negative Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges?

  14. Electric Charge II 1) have opposite charges 2) have the same charge 3) all have the same charge 4) one ball must be neutral (no charge) From the picture, what can you conclude about the charges?

  15. Conductors I 1) positive 2) negative 3) neutral 4) positive or neutral 5) negative or neutral A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positive-charged rod held near the ball. The charge of the ball must be:

  16. 1) 00 2) + – 3) – + 4) + + 5) – – 0 0 ? ? ConcepTest 21.2bConductors II Two neutral conductors are connected by a wire and a charged rod is brought near, butdoes not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors?

  17. Coulomb’s Law Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them.

  18. Coulomb’s Law Coulomb’s law: This equation gives the magnitude of the force between two charges.

  19. Coulomb’s Law Unit of charge: coulomb, C. The proportionality constant in Coulomb’s law is then: k = 8.99 x 109 N·m2/C2. Charges produced by rubbing are typically around a microcoulomb: 1 μC = 10-6 C.

  20. Coulomb’s Law Charge on the electron: e = 1.602 x 10-19 C. Electric charge is quantized in units of the electron charge.

  21. Coulomb’s Law The proportionality constant k can also be written in terms of ε0, the permittivity of free space:

  22. Coulomb’s Law The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same.

  23. F2 = ? F1 = 3 N Q Q Coulomb’s Law I 1) 1.0 N 2) 1.5 N 3) 2.0 N 4) 3.0 N 5) 6.0 N What is the magnitude of the force F2?

  24. Coulomb’s Law In its vector form, the Coulomb force is:

  25. Coulomb’s Law Which charge exerts the greater force? Two positive point charges, Q1 = 50 μC and Q2 = 1 μC, are separated by a distance . Which is larger in magnitude, the force that Q1 exerts on Q2 or the force that Q2 exerts on Q1?

  26. Coulomb’s Law Three charges in a line. Three charged particles are arranged in a line, as shown. Calculate the net electrostatic force on particle 3 (the -4.0 μC on the right) due to the other two charges.

  27. Solution:

  28. – 4Q +Q 3R Electric Force III 1) yes, but only if Q0is positive 2) yes, but only if Q0is negative 3) yes, independent of the sign (or value) of Q0 4) no, the net force can never be zero Two balls with charges +Q and –4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q0anywhereon the line such that the net force on Q0 will be zero?

  29. Coulomb’s Law Electric force using vector components. Calculate the net electrostatic force on charge Q3 shown in the figure due to the charges Q1 and Q2.

  30. Solution:

  31. Solution:

  32. +2Q 1 2 3 +4Q 4 d +Q 5 d Forces in 2D Which of the arrows best represents the direction of the net force on charge +Q due to the other two charges?

  33. Coulomb’s Law Make the force on Q3 zero. In the figure, where could you place a fourth charge, Q4 = -50 μC, so that the net force on Q3 would be zero?

  34. The Electric Field The electric field is defined as the force on a small charge, divided by the magnitude of the charge:

  35. The Electric Field An electric field surrounds every charge.

  36. The Electric Field For a point charge:

  37. The Electric Field Force on a point charge in an electric field:

  38. The Electric Field A photocopy machine works by arranging positive charges (in the pattern to be copied) on the surface of a drum, then gently sprinkling negatively charged dry toner (ink) particles onto the drum. The toner particles temporarily stick to the pattern on the drum and are later transferred to paper and “melted” to produce the copy. Suppose each toner particle has a mass of 9.0 x 10-16 kg and carries an average of 20 extra electrons to provide an electric charge. Assuming that the electric force on a toner particle must exceed twice its weight in order to ensure sufficient attraction, compute the required electric field strength near the surface of the drum.

  39. The Electric Field Electric field of a single point charge. Calculate the magnitude and direction of the electric field at a point P which is 30 cm to the right of a point charge Q = -3.0 x 10-6 C.

  40. Solution:

  41. -2 C 1 2 4 3 -2 C Superposition I What is the electric field at the center of the square? 5) E = 0

  42. -2 C -2 C 1 2 4 3 -2 C -2 C Superposition II What is the electric field at the center of the square? 5) E = 0

  43. -Q +Q 2 3 +Q 1 4 5 Superposition III What is the direction of the electric field at the position of the X ?

  44. The Electric Field E at a point between two charges. Two point charges are separated by a distance of 10.0 cm. One has a charge of -25 μC and the other +50 μC. (a) Determine the direction and magnitude of the electric field at a point P between the two charges that is 2.0 cm from the negative charge. (b) If an electron (mass = 9.11 x 10-31 kg) is placed at rest at P and then released, what will be its initial acceleration (direction and magnitude)?

  45. Solution:

  46. Solution:

  47. The Electric Field E above two point charges. Calculate the total electric field (a) at point A and (b) at point B in the figure due to both charges, Q1 and Q2.

  48. Solution:

  49. Solution:

  50. Solution: