1. Electric potential, Systems of charges
Physics 114
11/29/2018
Lecture IV

2. Concepts Primary concepts: Secondary concepts: Electric potential
Electric energy
capacitance
Secondary concepts:
Equipotentials
Electonvolt
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Lecture IV

3. Potential electric energy
High PE
High PE
Low PE
Low PE
Just like gravity electric force can do work
work does not depend on the path
it depends only on the initial and final position
 there is a potential energy associated with electric field.
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Lecture IV

4. Electric potential
PE/q is a property of the field itself – called electric potential V
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Lecture IV

5. Electric potential
V – electric potential is the potential energy of a positive test charge in electric field, divided by the magnitude of this charge q.
Electric potential is a scalar (so much nicer!).
Electric potential is measured in Volts (V=J/C).
Potential difference between two points DV=Vb-Va is often called voltage.
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Lecture IV

6. Charges in electric fields
E=const
Force on charge q:
F=qE
Work done by the field to move this charge
W=Fd=dqE
W=PEa-PEb=qVa-qVb=-qDV
d E=DV
E= DV/d, points from high potential to low
Sometimes electric field is measured in V/m =N/C b + a
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Lecture IV

7. Non-uniform electric field+
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8. Determine E from V Think ski slopes If V depends on one coordinate x
E is directed along x from high V to low
If V depends on x,y,z
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9. Electric field and potential in conductors
E=0 in good conductors in the static situation.
E is perpendicular to the surface of conductor.
Metal hollow boxes are used to shield electric fields.
When charges are not moving (!!) conductor is entirely at the same potential. + + + + + - - - - -
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Lecture IV

10. Electronvolt
Energy that one electron gains when being accelerated over 1V potential difference is called electronvolt eV:
1eV=1.6x10-19C 1V= 1.6x10-19J
Yet another unit to measure energy,
Commonly used in atomic and particle physics.
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Lecture IV

11. Equipontentials Equipotentials are surfaces at the same potential;
are always perpendicular to field lines;
Never cross;
Their density represents the strength of the electric field
Potential is higher at points closer to positive charge
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12. Potential of a point charge
Potential V of electric field created by a point charge Q at a radius r is
Q>0  V>0
Q<0  V<0
Do not forget the signs!
Potential goes to 0 at infinity.
Equipotentials of a point charge are concentric spheres. +
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Lecture IV

13. Superposition of fields
Principle of superposition:
Net potential created by a system of charges is a scalar (!) sum of potentials created by individual charges: + + - 1 2
Potential is a scalar 
no direction to worry about,
But signs are important.
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Lecture IV

14. Work to move a charge + + + -
How much work has to be done by an external force to move a charge
q=+1.5 mC
from point a to point b?
Work-energy principle +
30cm +
20cm
15cm
25cm + -
Q1=10mC
Q2=-20mC
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Lecture IV

15. Capacitance
Two parallel plates are called a capacitor. When capacitor is connected to a battery plates will charge up.
Note: net charge =0
C – coefficient, called capacitance, property of the capacitor.
Capacitance is measured in Farad (F=C/V)
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Lecture IV

16. Electric field in a capacitor
E=const
E= V/d
points from high potential to low
When V is fixed (same battery), E depends only on the d.
Potential
High next to + plate
Low – next to - plate
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Lecture IV

17. Capacitance Capacitance depends on the geometry of a capacitor
e0 = C2/N m2-
permittivity of free space
A – area of plates (m2)
Same sign charges want to “spread out” – to hold more charge need large area
d – distance between plates (m)
Opposite sign charges “hold” each other, attraction is stronger for shorter d A d
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Lecture IV

18. Dielectrics Put non-conductive material (dielectric) between plates
Can hold more charge  capacitance increases
K(>1) – dielectric constant
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19. Charging up a capacitor
Find the work needed to charge a capacitor C to voltage V
Take small charge dq and move it across the capacitor, which is at voltage V at this moment
dW=Vdq
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Lecture IV

20. Energy storage
Work to charge a capacitor= potential energy stored in the capacitor
To use the right formula, watch what is kept constant
V=const – if C connected to a battery
Q=const - if C disconnected
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21. Inserting dielectric
Capacitor is connected to a battery, supplying voltage V. How will the energy stored in the capacitor change if we insert a dielectric (K=2)?
CKC=2C – capacitance increases
V stays const – same battery
Q changes
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22. Inserting dielectric
Capacitor is charged to charge Q and disconnected from a battery. How will the energy stored in the capacitor change if we insert a dielectric (K=2)?
CKC=2C – capacitance increases
V can change
Q stays const – charge conservation
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23. Inserting dielectric Disconnected battery – Connected battery –
energy decreases
Dielectric will be
“sucked in”
Connected battery –
energy increases
Dielectric will be
“pushed out”
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Lecture IV

24. Test problem
Between two very large oppositely charged parallel plates at which of the three locations A, B and C electric potential is the greatest?
A A
B B
C C
D Equal at all three locations.
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25. E near metal sphere
Find the largest charge Q that a conductive sphere radius r=1cm can hold.
Air breakdown E=3x106V/m
Larger spheres can hold more charge
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26. Test problem What is wrong with this picture?
A Equipotentials must be parallel to field lines
B Field lines cannot go to infinity
C Some field lines point away from the negative charge
D Equipotentials cannot be closed
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Lecture IV