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Chapter 15 Conductors (again)

Chapter 15 Conductors (again). Lecture 16. 15 February 1999 Monday. Physics 112. The Physics 112 Help Session. Tuesdays 6:00 - 7:00 pm. Mondays 5:30 - 7:00 pm. NSC Room 118. Conductors (Revisited). What happens to a conductor when you place it in an electric field and allow the

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Chapter 15 Conductors (again)

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  1. Chapter 15 Conductors (again) Lecture 16 15 February 1999 Monday Physics 112

  2. The Physics 112 Help Session Tuesdays 6:00 - 7:00 pm Mondays 5:30 - 7:00 pm NSC Room 118

  3. Conductors (Revisited) What happens to a conductor when you place it in an electric field and allow the charges on it to attain equilibrium? conductor E (Remember, charges are free to move around on the surface of conductors.)

  4. 1) no electric field exists inside the conductor. What if it did? Then an electrical force would be exerted on the charges present in the conductor. In a good conductor, charges are free to move around, and will when a force is exerted on them. If charges are moving around, we are not in equilibrium. Contradiction!

  5. 2) Excess charges on an isolated conductor are found entirely on its surface. The 1/r2 nature of the electrostatic repulsive force is responsible for this one. The excess charges are trying to get as far away from one another as possible. It turns out, therefore, they all end up on the surface of the conductor.

  6. 3) The electric field just outside of a conductor must be perpendicular to the surface of the conductor. Again, what if this were not the case? Then a component of the electric field would exist along the conductor’s surface. This would yield an electrical force along the surface. As a good conductor, charges would move around in the presence of the force... Contradiction!

  7. E 4) On an irregularly shaped conductor, charges build up near the points (regions with smallest curvature). - - - - - - - - - - - - - Charges build up here: not as much room for them to move apart!

  8. The Book Says... In both cases, you are advised to THINK about the direction!

  9. Class Notes...

  10. To determine the direction of the , simply join point A to point B. The sign of their charges does not matter! B A Just connect the dots! points from the charge creating the field toward the charge of interest regardless of their signs! What is ?

  11. The notion of is just that of a coordinate system centered on the object of interest. z (x,y,z) q y f x We’re probably most familiar with the Cartesian coordinate system r or (r, q, f)

  12. z y points radially outward from theorigin of the coordinate system. x

  13. When you use (and only when you use this formulation) the signs of the charges become mathematically meaningful in the formulae you apply to the problems! If you use the book’s formulation, you must take the absolute values of the signs and THINK about the direction of the vector quantities you are calculating!!! Use whatever works for you!

  14. Chapter 16 Electrical Energy and Capacitance Recall that in the presence of the gravitational field, we defined potential energy and work done. This work could be done by any Newtonian force. We’ll now define similar quantities for electrical forces. We also examine the capacity of systems that hold charge.

  15. Conservative Forces

  16. Conservative Forces A force is conservative if the total work it does on a particle is zero when the particle moves exactly once around any closed path.

  17. The work done on a particle by a conservative force is independent of the path a particle takes to move from one point to another.

  18. Scalar quantity! No directions! Work = Force through a distance W = F|| d For the electrostatic force... W = qE d Electrical work is “Quite Easily Done!” NOTE: d is the distance parallel to the Electric field only!!! Project the electric field vector onto the displacement vector.

  19. d Example 1: r q E W = qE d NOT qE r !!!

  20. r q E d Example 2: W = qE d As long as the electric field is uniform, this is the answer!

  21. Recall: Potential Energy and Work are Related... Only valid in a uniform electric field! DPE = -W = -qE d Notice that work and potential energy are scalar quantities, NOT vectors! (i.e. they have no directional components) Example: speed is a scalar velocity is a vector

  22. Concept Quiz! Electrostatic Potential Energy

  23. A B A useful quantity in examining problems with charges is the electrical potential difference. This quantity is NOT the potential energy. Rather, the electrical potential difference is given by DV = Vb-Va = DPE/q DV is the change in potential energy per unit charge as the charge moves from point A to point B.

  24. Units! So, what are the units of V? DV = DPE/q So... [DV]=[DPE]/[q] [DV] = J/C = 1 Volt 1 Joule of energy is required to move 1 Coulomb of charge through a potential difference of +1 Volt.

  25. LOOK! DV = Vb - Va = DPE/q DPE = -W = -qE d REMEMBER, d is measured in direction of E only!!! DV = - qEd/q= -Ed NOTE: This ONLY works for a uniform electric field!! [DV] = [E] [d] 1 Volt = (N/C) m = J/C !

  26. DV = - E d, Wilbur! It’s EASY! Mr. Ed says...

  27. + Question: Does DV = -Ed in the field around a point charge? NO!

  28. What happens to the potential energy of a charge as it moves in the direction of the electric force? E +q d DECREASE! The electric field DOES work on + q, therefore, the potential energy must…...

  29. E +q d Va Vb Remember, the change in potential energy is minus the work done by the field force. What happens to the potential of a charge as it moves in the direction of the electric force?

  30. E +q d Va Vb Vb - Va = - E d It decreases in the direction of the electric field, REGARDLESS OF THE SIGN OF THE CHARGE!

  31. scalar! So, how’s this work for point charges? First, assume that the potential in the field of a point charge is ZERO at infinity (we did something similar for gravity, right?) Use Calculus…. VOILA!

  32. NOTE: V > 0 around positive charges V < 0 around negative charges Also... The superposition principle applies to potentials! Vtot = V1 + V2 + V3 + ...

  33. Concept Quiz! Electrostatic Potential

  34. How much work do we do in bringing a point charge (q2) from infinity to a distance r from point charge q1? q1 q2 r

  35. NOTE: PE > 0 for LIKE charges PE < 0 for opposite charges You could probably have guessed that PEtot = PE1 + PE2 + PE3 + ...

  36. Fe A B +q E d What happens to the potential energy of a positive charge (+q) as it moves in the direction of the electric field? DPE = - qE d = - (+q) E d = - qE d

  37. Fe A B -q E d What happens to the potential energy of a negative charge (-q) as it moves in the direction of the electric field? DPE = - q E d = - (-q) E d = + qE d

  38. Fe A B +q E d What happens to the potential of a positive charge (+q) as it moves in the direction of the electric field? DV = - E d

  39. Fe A B -q E d What happens to the potentialof a negative charge (-q) as it moves in the direction of the electric field? DV = - E d

  40. The electrical potentialALWAYS decreasesin the direction of the electric field! It does not depend upon the sign of the charge. The electrical potential energy depends upon the sign of the charge. It decreases in the direction of the electrical force.

  41. p 1 m q1 2 m q2 q1 = +2 mC q2 = -5 mC Example: What is the potential at point p? Vtot = V1 + V2

  42. p 1 m q1 2 m q2 q1 = +2 mC q2 = -5 mC Example: What is the potential at point p? Vtot = V1 + V2 V1 = 18,000 V V2 = -20,125 V Vtot = -2,125 V

  43. p 1 m q1 2 m q2 q1 = +2 mC q2 = -5 mC Example: How much work is required to bring a 5 mC charge from infinity to point p? W= (5 X 10-6 C) (-2,125 V) = -1.1 X 10-2 J

  44. Equipotential Surfaces An equipotential surface is a set of points in an electric field which are all at the same electrical potential. One example is the locus of points equidistant from an isolated point charge. Electric field lines Equipotential surfaces

  45. Notice that the equipotential surfaces are perpendicular to the electric field lines everywhere! Remember that work is only done when a charge moves parallel to the electric field lines. So no work is done by the electric field as a charge moves along an equipotential surface. This is just like GRAVITY, right?

  46. The potential difference between any two points on an equipotential surface (Vb - Va ) must be... 0

  47. Conductors When in electrostatic equilibrium (i.e., no charges are moving around), all points on and inside of a conductor are at the same electrical potential!

  48. Conductors Remember that the electric field is everywhere perpendicular to the surface of a conductor, and is zero inside of a conductor. So, from the surface of a conductor throughout its interior the electric field is 0 when the conductor is in electrostatic equilibrium. DV = - E d = 0

  49. +Q d -Q Capacitors A common type of capacitor consists of a pair of parallel conducting plates, one charged positively, one charged negatively.

  50. +Q E d -Q Capacitors An electric field exists between the plates of a capacitor. Therefore….

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