Electricity and Magnetism
• Electric Potential
– Electric Field and Electric Potential
– Capacitors
Mar 4 2002
More on Electric Potential
• Where do charges go?
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More on Electric Potential
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More on Electric Potential
• Practical application
– Lightning rod: Pointy tip -> small r!
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Charge and Potential
• Potential is proportional to Charge
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2*kQ/R
V=kQ/R
R
Mar 4 2002
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Charge and Potential
• Potential is proportional to Charge
– V * constant = Q
• True for any object
– true for point charge
– Superposition principle
• Define
– Q = C V -> C is called Capacitance
Mar 4 2002
Capacitance
• [Capacitance] = [C/V] = Farad
– 1 Farad is huge
• Sphere
– C = R/k
– The bigger the sphere, the bigger the
capacitance
Mar 4 2002
Capacitance
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slope = 1/C
C small
C big
Q
Q = C*V => V = Q/C
Mar 4 2002
Capacitance
• Example C(Earth):
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C = 6*106m /9*109 Nm2/C2 = 540 µFarad
Small capacitance
Potential increases quickly with charge
Hard to put charge on sphere
For sphere, reference point is r=infinity
How to build better device?
Mar 4 2002
Capacitor
• Better capacity
– don’t get charges from infinity, but from other
object close-by
• Capacitor
– Def: Two conductors separated by insulator
• Example: Parallel plate capacitor
Mar 4 2002
Parallel Plate Capacitor
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Parallel Plate Capacitor
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Parallel Plate Capacitor
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C = ε0 A/d
• Depends only on
Geometry!
– like it did for sphere
• To store lots of charge
– make A big
– make d small
Parallel Plate Capacitor
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Mar 4 2002
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slope = 1/C
C=ε0 A/d
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