Unformatted text preview: o charged objects, then
the capacitance with a dielectric, K, is related to the capacitance with a vacuum (or air) in
between by the formula C = K*C_air
So a more typical capacitor problem for a final would be:
Two concentric cylindrical metal plates contain equal and opposite charge with linear
charge density, lambda. Initially, air fills the space between the charged plates.
a) What is the electric potential at r=b? It is zero since E
field outside is 0 and we usually
define V=0 at r=infinity for charge distributions where the E
field fades out at large
distances. Since E=0 outside, there is no change of potential so it must remain 0.
b) Find the Electric field between the plates in terms of lambda, epsilon0, a, b
c) Find the change of electric potential between the plates in terms of...
d) Find the capacitance of the object
e) Suppose a dielectric material of dielectric constant K is uniformly fills the volume
between the plates, what is the new capacitance? Quiz A for 7D Week #5
Name: __________________
ID: __________________
1. A concentric cylinder and cylindrical shell of length L are shown below. They carry equal
and opposite charges with the inner cylinder possessing a uniform charge density, ρ.
From this information and the diagram, please calculate the following:
(Note: Assume no edge effects) a) The electric potential at the outer cylinder, r = b. b) The change in electric potential from the inner cylinder to the outer cylinder. c) The capacitance of the cylinders d) How would capacitance change if we added a dialectric with constant K? 2. Suppose you have an electric dipole composed of two equal charges, +q and 
q,
separated by a distance, d. In an E
field strength E oriented at 30o from parallel, Quiz B for 7D Week #5 Name: __________________
ID: __________________
1. A concentric cylinder and cylindrical shell of length D are shown below. They carry equal
and opposite charges with the inner cylinder possessing a uniform charge density, 
η (eta
is a constant).
From this and the diagram, please calculate the following:
(Note: Assume no edge effects)
a) The electric potential at the outer cylinder, r = b. b) The change in electric potential from the inner cylinder to the outer cylinder. c) The capacitance of the cylinders d) How would capacitance change if we added a dialectric with constant, K? 2. Suppose you have an electric dipole composed of two equal charges, +q and 
q,
separated by a distance, r. In an E
field strength E oriented at 45o from parallel, calculate
the torque on the dipole. Solutions to Quiz Form A:
1a) There is an easy way answer to this question. For charge distributions that
you know give an E
field that fades to nothing at infinity, the usual thing is
to define the Electric potential to be 0 at infinity. Now since the E
field for
r>b is 0 (the net charge enclosed by a Gaussian cylinder is zero for r of
gaussian cylinder greater than b), you know that the electric potential
cannot change at any point outside of the cylinder of radius b.
1b) The change in potential we calculate from the definite integral of E
Field from a to b :
q Electric field from Gauss’ Law for r>a and r<b: E * A = εo E * 2πrL =
E = ΔV = − ρ(πLa2)
εo ρ(a2)
2rεo ;7 a <r<b ρ(a2) ln( b )
a
2εo 1c) The capacitance follows: C = Q/V C = ρ(πa2L)
ρ(a2) ln( b )
a
2εo π
L
C = 2n(Lε)o , d) C = 2πn(ε )K
l
lb
a o
b
a 2) Comes straight from the book: E*q*d*sin(30)
Solutions to Form B:
1a) There is an easy way answer to this question. For charge distributions that you know give
an E
field that fades to nothing at infinity, the usual thing is to define the Electric potential to be 0
at infinity. Now since the E
field for r>b is 0 (the net charge enclosed by a Gaussian cylinder is
zero for r of gaussian cylinder greater than b), you know that the electric potential cannot change
at any point outside of the cylinder of radius b. 1b) Electric field from Gauss’ Law: E*A= q
εo E * 2πrD =
E = −η(πDa2)
εo −η(a2)
2rεo ;7 a <r<b The change in potential we calculate from the definite integral of E
Field from a to b:
(Negatives cancelled) ΔV = η(a2) ln( b )
a
2εo 1c) The capacitance follows: C = Q/V C = ρ(πa2D)
ρ(a2) ln( b )
a
2εo D
C = 2lπDεo , d) C = 2πln(ε )K
n( b )
a 2) Comes straight from the book: q*r*E*sin(45) o
b
a...
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This note was uploaded on 09/23/2013 for the course PHYSICS 7D 7D taught by Professor Barwick during the Spring '11 term at UC Irvine.
 Spring '11
 Barwick

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