Physics 212 Lecture 7, Physics 212 Lecture 7, Slide Slide 1 Physics 212 Physics 212 Lecture 7 Lecture 7 Today's Concept: Today's Concept: Conductors and Conductors and Capacitance Capacitance How are charges distributed on conductors? How are charges distributed on conductors? What is capacitance and how can we What is capacitance and how can we calculate it? calculate it?
19
Embed
Physics 212 Lecture 7, Slide 1 Physics 212 Lecture 7 Today's Concept: Conductors and Capacitance How are charges distributed on conductors? What is capacitance.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Conductors and CapacitanceConductors and Capacitance
How are charges distributed on conductors? How are charges distributed on conductors? What is capacitance and how can we calculate it?What is capacitance and how can we calculate it?
Main Point 1
First, charges in a conductor will always move so as to create a zero electric field at all points in the conductor. Consequently, all conductors are equipotentials and the electric field at the surface of a conductor is always perpendicular to that surface.
Second, the capacitance C of a system composed of two spatially separated conductors (called a capacitor) is defined in terms of the potential difference V between the conductors that is produced when each conductor carries an equal amount Q of oppositely signed excess charge. In particular, C is defined to be equal to Q/V.
Third, energy is stored in electric fields. The energy density (i.e., the energy per unit volume) present in an electric field E is proportional to the square of the electric field (i.e., u = ½ e0E2). When a capacitor is charged, it has an energy U stored in the electric field between the conductors which is proportional to the product of the potential difference between the conductors and the separated charge (i.e., U = ½ QV)
Two spherical conductors are separated by a large distance. They each carry the same positive charge Q. Conductor A has a larger radius than conductor B.
Compare the potential at the surface of conductor A with the potential at the surface of conductor B.A. VA > VB B. VA = VB C. VA < VB
Two parallel plates of equal area carry equal and opposite charge Q0. The potential difference between the two plates is measured to be V0. An uncharged conducting plate (the green thing in the picture below) is slipped into the space between the plates without touching either one. The charge on the plates is adjusted to a new value Q1 such that the potential difference between the plates remains the same.
A) CA) C11 > C > Coo B) CB) C11 = C = Coo C) CC) C11 < C < Coo
Two parallel plates of equal area carry equal and opposite charge Q0. The potential difference between the two plates is measured to be V0. An uncharged conducting plate (the green thing in the picture below) is slipped into the space between the plates without touching either one. The charge on the plates is adjusted to a new value Q1 such that the potential difference between the plates remains the same. What happens to C1 relative to C0?
CapacitanceCapacitanceCapacitance is defined for any pair of spatially separated Capacitance is defined for any pair of spatially separated conductorsconductors
99
QC
V
How do we understand this definition ???How do we understand this definition ???
+Q+Q
-Q-Q
dd
• Consider two conductors, one with excess charge = +Q Consider two conductors, one with excess charge = +Q and the other with excess charge = -Qand the other with excess charge = -Q
• These charges create an electric field in the space between These charges create an electric field in the space between themthem
EE
• This potential difference should be proportional to Q !!This potential difference should be proportional to Q !!• The ratio of Q to the potential difference is the capacitance The ratio of Q to the potential difference is the capacitance and only depends on the geometry of the conductorsand only depends on the geometry of the conductors
VV
• We can integrate the electric field between them to find the We can integrate the electric field between them to find the potential difference between the conductorpotential difference between the conductor
Example ProblemExample ProblemTwo parallel plates of area Two parallel plates of area AA separated by a distance separated by a distance dd carry equal an carry equal an opposite charge opposite charge QQ00. An uncharged conducting plate having thickness . An uncharged conducting plate having thickness tt is slipped midway between the plates.is slipped midway between the plates.