1. 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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2. 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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3. 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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4. Uniform Charge Density: Summary
Cylindrical
symmetry
Planar
Spherical
Non-conductor
Conductor
inside
outside
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5. 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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6. 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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7. 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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8. 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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9. 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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10. 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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11. 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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12. 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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13. Potential & Electric Fields
The electric field points in the direction in which the potential decreases most rapidly.
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14. 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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15. 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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16. 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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17. V(r) versus r for a positive charge at r = 0to r
For a point charge
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18. Electrical Potential Energy
Push q0 “uphill” and its electrical potential energy increases according to
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19. + Demos: R + + V(r) + R + + + + + + +
Gauss’ law says the sphere looks like a point charge outside R.
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20. Demo + + + 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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21. 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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22. 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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23. Calculating the Electric Field from the Potential Field
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24. 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