1. Question 3.
A solid conducting sphere is concentric with a thin conducting shell, as shown.
The inner sphere carries a charge Q1, and the spherical shell carries a charge Q2, such that Q2 = -3Q1. R1 R2 Q1 Q2
What is the electric field at r < R1? A) B) C)
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2. Question 4.
A solid conducting sphere is concentric with a thin conducting shell, as shown.
The inner sphere carries a charge Q1, and the spherical shell carries a charge Q2, such that Q2 = -3Q1. R1 R2 Q1 Q2
What is the electric field at R1<r < R2? A) B) C)
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3. Question 5.
A solid conducting sphere is concentric with a thin conducting shell, as shown.
The inner sphere carries a charge Q1, and the spherical shell carries a charge Q2, such that Q2 = -3Q1. R1 R2 Q1 Q2
What is the electric field at R2<r A) B) C)
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4. Question 6 R1 R2 Q1 Q2
A solid conducting sphere is concentric with a thin conducting shell, as shown.
The inner sphere carries a charge Q1, and the spherical shell carries a charge Q2, such that Q2 = -3Q1.
What happens when you connect the two spheres with a wire?
(A) The charge is uniformly distributed on the outside surface of the shell.
(B) There is no charge on the sphere or the shell.
(C) The charge is uniformly distributed on the outer surfaces of the sphere and the shell.
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5. Example E Compare the electric field at point X in cases A and B:
Consider the following two topologies:
A) A solid non-conducting sphere carries a total charge Q = -3 C distributed evenly throughout. It is surrounded by an uncharged conducting spherical shell. s2 s1 -Q E
B) Same as (A) but conducting shell removed
Compare the electric field at point X in cases A and B:
(a) EA < EB
(b) EA = EB
(c) EA > EB
Select a sphere passing through the point X as the Gaussian surface.
How much charge does it enclose?
Answer: -Q, whether or not the uncharged shell is present. (The field at point X is determined only by the objects with NET CHARGE.)
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6. Conductors: External Electric Field
For a spherical conductor, excess charge distributes itself uniformly
For a non-spherical conductor, the surface density varies over the surface & makes the E field difficult to determine.
However, the E field set-up just outside the conductor is easy to determine.
Examine a tiny portion of a large conductor with an excess of positive charge.
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7. Two Parallel Conducting Sheets
Find the electric field to the left of the sheets, between the sheets and to the right of the sheets.
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8. Uniform Charge Density: Summary
Cylindrical
symmetry
Planar
Spherical
Non-conductor
Conductor
inside
outside
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9. Summary of Lectures 3, 4 & 5
*Relates net flux, F, of an electric field through a closed surface to the net charge that is enclosed by the surface.
*Takes advantage of certain symmetries (spherical, cylindrical, planar)
*Gauss’ Law proves that electric fields vanish in conductor, extra charges reside on surface
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10. Lectures 6 & 7: Chapter 23 Electric Potential Definitions Examples C BV Q
4pe0 r
4pe0 R
Definitions
Examples C B r B A r q A
Equipotential
surfaces
Path independence
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11. From Mechanics (PHYS 172) Energy Conservative Forces:
Kinetic Energy: associated with the state of motion
Potential Energy: associated with the configuration of the system
Work done by a conservative force is independent of path
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12. From Mechanics (PHYS 172) Work F W > 0 dr W < 0 F dr F W = 0 dr
Object speeds up ( DK > 0 )
W < 0
Object slows down (DK < 0 ) F dr or F dr
W = 0
Constant speed (DK = 0 )
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13. Electric Potential Energy
When an electrostatic force acts between two or more charges within a system, we can assign an Electric Potential Energy: F + + Dx + +
If a Coulomb force does negative work
Potential energy increases
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14. Question
You hold a positively charged ball and walk due west in a region that contains an electric field directed due east. +
West E
East
WH is the work done by the hand on the ball
WE is the work done by the electric field on the ball
Which of the following statements is true:
A) WH > 0 and WE > 0
B) WH > 0 and WE < 0
C) WH < 0 and WE < 0
D) WH < 0 and WE > 0
Work by hand is positive
Work by electric field is negative
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15. Example: Electric Potential Energy
What is the change in electrical potential energy of a released electron in the atmosphere when the electrostatic force from the near Earth’s electric field (directed downward) causes the electron to move vertically upwards through a distance d?
U of the electron is related to the work done on it by the electric field:
Work done by a constant force on a particle undergoing displacement:
Electrostatic Force and Electric Field are related:
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16. Example: Electric Potential Energy
What is the change in electrical potential energy of a released electron in the atmosphere when the electrostatic force from the near Earth’s electric field (directed downward) causes the electron to move vertically upwards through a distance d?
U of the electron is related to the work done on it by the electric field:
Work done by a constant force on a particle undergoing displacement:
Electrostatic Force and Electric Field are related:
Key Idea:
Key Idea:
Key Idea:
Electric potential decreases as electron rises.
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17. Electric Potential versus Electrical Potential Energy
Electric Potential is a property of an electric field and is measured in J/C or V
Electric Potential Energy is an energy of system consisting of the charged object and the external electric field, and is measured in Joules.
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18. Potential & Electric Fields
The electric field points in the direction in which the potential decreases most rapidly.
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19. Example: Potential Difference
*independent of path
(a) What is V moving directly from point i to point f? i c f
(b) What is V moving from point i to point c to point f?
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20. Question: x ´ -Q (a) VBA < 0 (b) VBA = 0 (c) VBA > 0
A single charge ( Q = -1C) is fixed at the origin. Define point A at x = + 5m and point B at x = +2m.
What is the sign of the potential difference between A and B?
Where VBA = VB-VA x
-1C A B -Q
(a) VBA < 0
(b) VBA = 0
(c) VBA > 0
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21. Potential due to a point charge:
Find V in space around a charged particle relative to the zero potential at infinity: +
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22. V(r) versus r for a positive charge at r = 0to r
For a point charge
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23. Electrical Potential Energy
Push q0 “uphill” and its electrical potential energy increases according to
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24. + Demo 5A-16 R + + V(r) + R + + + + + + +
Gauss’ law says the sphere looks like a point charge outside R.
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25. Demo 5A-35 + + + R + + r1 r2 + + + + + + across fluorescent light bulb
Get energy out
charge flow + + + R + + r1 r2 + + + + + +
across fluorescent
light bulb
Also try an
elongated neon bulb.
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26. Potential due to a Group of Point Charges
Find the Potential at the center of the square.
q1 = +12 nC
q2 = -24 nC + -
d = 1.3 m
q3 =+31 nC
q3 =+17 nC
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27. Electrical Potential Energy of a System of Point Charges
U of a system of fixed point charges equals W done by an external agent to assemble the system by bringing each charge in from infinity. +
If q1 & q2 have the same sign, we must do positive work to push against mutual repulsion.
If q1 & q2 have opposite signs, we must do negative work against mutual attraction
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28. Calculating the Electric Field from the Potential Field
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29. Potential Energy of an Electric Dipole
Potential energy can be associated with the orientation of an electric dipole in an electric field.
U is least =0 U=-pE
U is greatest =180 U=pE
U =0 when =90