1. Electric dipole, systems of charges
Physics 122
9/22/2018
Lecture III

2. Workshops
Due to low interest – 4 people and very limited resources I have to cancel one of the workshops:
Fridays, 4-6 pm B&L 108A 
Please let me know alternative times I’ll switch you to other workshops
9/22/2018
Lecture III

3. I am running Rochester marathon
This Saturday, September 17, 8:00 am
Starts and ends at Frontier field
Goes along East and returns on Park Ave
Lots of coffee shops and sit back, relax and watch people suffer
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Lecture III

4. Concepts Primary concepts: Secondary concepts: Electric field
Electric dipole
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5. Laws Dipole field Dipole in electric field: energy and torque
Superposition principle for a continuous distribution of charge
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6. Skills Calculate electric field of a system of charges 9/22/2018
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7. Electric field + + F – force between two charges(N)
Q – electric charge (C= Coulomb)
E – electric field created at point 1 by charge 2
Charge 2 has changed the property of space at point 1
Charge 1 is experiencing this change + + 1 2
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8. Superposition of fields
Principle of superposition:
Net field created by a system of charges is a vector sum of fields created by individual charges:
Positive test charge + + - 1 2
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9. Electric dipole -Q +Q l
Two opposite charges of equal value Q separated by distance l
Define dipole moment:
A vector directed from negative charge to positive.
Example – water molecule p1 H+
--O p H+ p2
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10. Electric Dipole Field Linesy
Lines leave positive charge and return to negative charge
What can we observe about E?
Ex(x,0) = 0
Ex(0,y) = 0 x
Field largest in space between two charges
We derived: for r >> L,
Demo Eb-1 (place on overhead, charge w/ Whimshurst) at the start. Note where there is symmetry
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11. Torque Force makes objects move  torque makes objects rotate
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12. How to add torques? + - You have to think…
If the force acts to rotate the system
counterclockwise – torque and angular acceleration are positive
clockwise – torque and angular acceleration are negative
Only relative sign matters + -
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13. How to add torques? + - Axis of rotation Axis of rotation 9/22/2018
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14. How to add torques? - + Axis of rotation Axis of rotation 9/22/2018
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15. Electric dipole Dipole in uniform E Net force F=F+-F-=0 Net torque
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16. Electric dipole Dipole in uniform E Energy - ? Work done by the field
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17. Energy of dipole in electric field-Q +Q -Q +Q -Q +Q
Lowest energy state – dipole parallel to the field
In electric field dipoles line up with the field
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18. Dipole in electric field-Q +Q
In electric field dipoles line up with the field
Dipole internal field anti-parallel in external field
Net field is reduced
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19. Test question E - +
If this region is filled with pure water (an excellent insulator), does the electric field…
Increase?
Decrease?
Remain the same E - +
The positive charge is shielded by the negative charges of the aligned dipoles (and vice versa).
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20. The Electric Field of a system of charges
Bunch of Charges
Charge Distribution + - + + + + + + + + + + +
E=F/q. Superposition gives the sum (or integral!)
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21. Vectors by components r dq
Charge Distribution r dq +
E=F/q. Superposition gives the sum (or integral!)
r, q are different for different charges and
depend on your definition of the coordinate system,
So choose it wisely
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22. Symmetry and coordinate systems
Coordinate systems are there to help you
You have a choice of
System type
Cartesian
Cylindrical
Spherical
Origin (0,0), Direction of axis
A good choice (respecting the symmetry of the system) can help to simplify the calculations
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23. Ring of charge
A thing ring of radius a holds a total charge Q. Determine the electric field on its axis, a distance x from its center. a x q
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24. Charged disk
Disk of radius R, uniformly charged with Q, determine E on the axis, a distance z above the center.
Define charge density
s =Q/pr2
Reuse previous results – divide disk into rings radius r, integrate over r from 0 to R. z
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25. Two parallel plates + - Infinite plates One positive, one negative,
Same charge density s + -
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26. Long line of charge
Determine the magnitude of the electric field at a distance x from a very long wire of uniformly distributed charge with linear charge density l (C/m).
dq=ldy y q x
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