1. Exam #1
Attention: Midterm test #1 will be given in Lecture class on Wednesday October 5 starting at noon.
One hour long
For students requiring extra time:
Please contact the Learning Assistance Services
Fill the form, let me sign it and arrange the time for your test
If you have a conflict with a religious holiday – alternative time – Monday 10/3 – 3pm
Sign up after class
11/15/2018
Lecture VI

2. 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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3. 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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4. E near metal sphere
Find the largest charge Q that a conductive sphere radius r=1cm can hold.
Air breakdown E=3x106V/m
Near surface: E=V/r Larger spheres can hold higher voltage
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5. Capacitance
Physics 122
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6. Concepts Primary concepts: Capacitor and capacitance
Storing electric energy and charge
Dielectrics
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7. Laws Charge on a capacitance Capacitance formula
Capacitance with dielectric
Energy in a capacitance
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8. 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 VI

9. 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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10. 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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11. Dielectrics Put non-conductive material (dielectric) between plates
Can hold more charge  capacitance increases
K(>1) – dielectric constant
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12. 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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13. 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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14. 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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15. 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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Lecture VI

16. 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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17. 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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18. Capacitor connections
Three capacitors connected to a battery in Parallel:
Same voltage at capacitors C1, C2, C3
V1=V2=V3=V
Different charges:
Q1=C1V
Q2=C2V
Q3=C3V
Total charge stored on three capacitors:
Q=Q1+Q2+Q3=V(C1+C2+C3)
Ceq=C1+C2+C3
No DC current
through capacitor,
Just store charge.
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19. Capacitor connections
Three capacitors connected in series
Same charge on each capacitor
(QA=0  -Q1+Q2=0)
Q1=Q2=Q3
Different voltages V=V1+V2+V3
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