Conductors & Electric Fields
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1 Conductors & Electric Fields suppose you have a conductor (that may have charge on it) any electric field in the bulk of it would cause charges to move therefore: electric field is zero inside a conductor in equilibrium lecture 4.2.1
2 Conductors & Electric Fields suppose you have a conductor (that may have charge on it) any electric field in the bulk of it would cause charges to move therefore: electric field is zero inside a conductor in equilibrium consider a Gaussian surface just inside the surface of the conductor zero E means by Gauss s Law lecture therefore: all charge resides on the surface
3 Conductors & Electric Fields there is an electric field outside of a charged conducting surface but if it had any component parallel to the surface, charges would move lecture 4.2.3
4 Conductors & Electric Fields there is an electric field outside of a charged conducting surface but if it had any component parallel to the surface, charges would move therefore: electric fields just outside the surface of a conductor must be perpendicular to the surface lecture 4.2.4
5 Conductors & Electric Fields lecture 4.2.5
6 Conductors & Electric Fields Use these facts to determine the electric field outside the surface of a charged conductor. Φe = AEsurface = Qin/ϵ0 Qin = σa where σ is the surface charge density of the conductor. lecture 4.2.6
7 Conductors & Electric Fields What happens when you bring an external charge near a conductor? Electric field is zero inside the conductor. lecture 4.2.7
8 Conductors & Electric Fields consider a charged conductor with a hole inside. E=0 inside the conductor, so Qin = 0 for the interior surface. therefore E=0 in the hole as well lecture 4.2.8
9 Conductors & Electric Fields A conducting sphere is placed in a uniform electric field. What will happen to charges in the sphere? lecture 4.2.9
10 Conductors & Electric Fields The charges move until the interior field is zero. lecture
11 Conductors & Electric Fields The charges move until the interior field is zero. lecture
12 Conductors & Electric Fields lecture
13 Conductors & Electric Fields consider a charged conductor with a hole inside, with a charge in the hole: lecture
14 Conductors & Electric Fields lecture
15 Conductors & Electric Fields lecture
16 Conductors & Electric Fields Charge +3 nc is in a hollow cavity inside a large chunk of metal that is electrically neutral. The total charge on the exterior surface of the metal is A. 0 nc B. +3 nc C. 3 nc D. Can t say without knowing the shape and location of the hollow cavity. lecture
17 Conductors & Electric Fields Charge +3 nc is in a hollow cavity inside a large chunk of metal that is electrically neutral. The total charge on the exterior surface of the metal is A. 0 nc B. +3 nc C. 3 nc D. Can t say without knowing the shape and location of the hollow cavity. lecture
18 Conductors & Electric Fields lecture
19 Conductors & Electric Fields lecture
20 Conductors & Electric Fields charge on a conductor concentrates at regions of high curvature lightning rods will allow charge to leak off to the atmosphere lecture
21 Conductors & Electric Fields charge on a conductor concentrates at regions of high curvature lightning rods will allow charge to leak off to the atmosphere corona discharge (known to sailors as St. Elmo's Fire) lecture
22 Conductors & Electric Fields lecture
23 Chapter 7: Electric Potential 1 Electric Potential Energy 2 Electric Potential 3 Calculations of Electric Potential lecture Determining Field from Potential 5 Equipotential Surfaces & Conductors 6 Applications of Electrostatics
24 Work and Energy Two rocks have equal mass. Which has more gravitational potential energy? A. B. C. D. Rock A Rock B They have the same potential energy. Both have zero potential energy. lecture
25 Two rocks have equal mass. Which has more gravitational potential energy? A. B. C. D. Increasing PE Rock A Rock B They have the same potential energy. Both have zero potential energy. lecture
26 Work and Energy kinetic energy of a system: a system s change in potential energy, ΔU, is the negative of the work done by all internal (interaction) forces: with conservative forces the total energy Emech= K + U is conserved lecture
27 Work and Energy lecture
28 Work and Energy lecture
29 Work and Energy The change in gravitational potential energy is ΔUgrav = Wgrav where Ugrav = U0 + mgy lecture
30 Work and Energy The work done is Welec = qesi qesf The change in electric potential energy is ΔUelec = Welec where Uelec = U0 + qes lecture
31 Work and Energy Two positive charges are equal. Which has more electric potential energy? A. B. C. D. Charge A Charge B They have the same potential energy. Both have zero potential energy. lecture
32 Work and Energy Two positive charges are equal. Which has more electric potential energy? A. B. C. D. Charge A Charge B Increasing PE They have the same potential energy. Both have zero potential energy. lecture
33 Work and Energy Objects always fall toward lower potential energy. lecture
34 Work and Energy an energy diagram for a positively charged particle in a uniform electric field total mechanical energy Emech is fixed. lecture
35 Work and Energy Objects always fall toward lower potential energy. lecture
36 Work and Energy Two negative charges are equal. Which has more electric potential energy? A. B. C. D. Charge A Charge B They have the same potential energy. Both have zero potential energy. lecture
37 Work and Energy Two negative charges are equal. Which has more electric potential energy? A. B. C. D. Charge A Charge B They have the same potential energy. Both have zero potential energy. lecture Increasing PE for negative charge
38 Work and Energy A positive charge moves as shown. Its kinetic energy A. Increases. B. Remains constant. C. Decreases. lecture
39 Work and Energy A positive charge moves as shown. Its kinetic energy A. Increases. B. Remains constant. C. Decreases. lecture Increasing PE Decreasing KE
40 Work and Energy For a non-uniform field... Find the work done to move charge q2 from xi to xf : lecture
41 Work and Energy For a non-uniform field... Find the work done to move charge q2 from xi to xf : lecture
42 Electric Potential Energy Two point charges, q1 and q2, separated by a distance r store an electric potential energy of The Potential Energy of Point Charges This is explicitly the energy of the system, not the energy of just q1 or q2. Note that the potential energy of two charged particles approaches zero as r. lecture
43 Electric Potential Energy lecture
44 Electric Potential Energy lecture
45 Electric Potential Energy lecture
46 Electric Potential Energy The work done on q2 (and the change in potential energy) is path independent. lecture
47 Electric Potential Energy Going to P1 to P2 independent of path taken. lecture
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