5/18/2011
PHY 2049: Class Quiz
PHY 2049: Physics II
Coulomb’s law,
electric field, Gauss’
theorem and electric
potential.
-W = q∆V
Energy conservation
applies.
F =−
F
∂U
U
∂x
F = qE
U = qV
E=−
E
∂V
∂x
V
If 500 J of work are required to carry a charged
particle between two points with a potential
difference of 20V, the magnitude of the charge on
the particle is:
A. 0.040C
B. 12.5C
C. 20C
D. cannot be computed unless the path is given
E. none of these
PHY 2049: Physics II
PHY 2049: Physics II
Calculate the Electric Field at P
Calculate the el. potential at P
Ex =
2kq 
1 
51 −

d2  2 2 
2 kq 3
d2 2 2
kq
V = −4
d
Ey =
What is the potential at the center point (in units of kq/d) ?
a) -7 (b) -5 (c) -7 (d) -7
PHY 2049: Physics II
•Point charge
V =k
q
r
qi
ri
•Distribution of charges
= k∑
•Line charge at an edge
l + l 2 + d 2 
= kλ ln 

d


•Disc on an axis through
the center
i
=
σ
2ε o
( z 2 + R 2 − z)
Some old business:
What is the electric field
of a shell
of a uniform spherical charge distribution?
What is the potential for each of the above?
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5/18/2011
PHY 2049: Physics II
E
R
V
r
Some old business
The potential of a
uniform spherical
charge.
Calculate electric
field, integrate it to
get the potential
V
k
8q 2
a
II E = 1.6 kq21 ,
a
Two particles with charges Q and -Q are
fixed at the vertices of an equilateral
triangle with sides of length a. The work
required to move a particle with charge q
from the other vertex to the center of the
line joining the fixed particles is:
A. 0
B. kQq/a
C. kQq/a2
D. 2kQq/a
E. 1.4kQq/a
V=
PHY 2049: Physics
26.6°
a= 39 cm
q1 = 3.4pC
q2 = 6 pC
E at the center?
What is the
potential at the
center?
PHY 2049: Physics II
PHY 2049: Physics II
An outline
Capacitors, plate, coaxial, spherical..
Energy, Dielectric strength, Dielectric
constant.
Netweorks: Parallel and Series configuration.
PHY 2049: Physics II
Capacitors: A device to hold charge.
It is held by Coulomb force between the
charges. +q and –q on two separate
places.
V : potential difference: q= CV
C: capacitance units farad.
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5/18/2011
PHY 2049: Physics II
Potential near a sheet charge
V ( z ) = − ∫ E.dz + Const
= V+ −
∆ V = Ed =
C = εo
σ
d
εo
σ
2ε o
z
A
d
Potential near a sheet charge
PHY 2049: Physics II
V ( z ) = − ∫ E.dz + Const
= V+ −
σ
z
εo
V+ − V− =
Q
d
εo A
C = εo A / d
PHY 2049: Physics II
E (r ) = −
λ 1
2πε o r
E=k
Va − Vb =
λ
ln r
2πε o
Q
2πε o h
ln
q
r2
V (r ) = k
V (r ) = − ∫ E.dr
=−
PHY 2049: Physics II
b
a
q
r
1 1
Va − Vb = kq  − 
a b
 ab 
C = 4πε o 
 ⇒ 4πε o R
b−a
C = 2πε o h ln(b / a )
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5/18/2011
HITT
A uniform electric field, with a magnitude
of 600 N/C, is directed parallel to the
positive x-axis. If the potential at x = 3.0
m is 1000 V, what is the potential at x =
1.0 m?
PHY 2049: Physics II
What is the capacitance of various familiar
balls.
C = 4πεoR = 10-10 R(m) F
a. 400 V
b. 1600 V
c. 2200 V
Basketball-it is an insulator
Van de Graff top
Earth (radius 6.4 X 106 m)
d. 2500 V
PHY 2049: Physics II
CE = 0.71 mF
PHY 2049: Physics II
Energy stored in a capacitor
U = ½ CV2 = Q2/2C = ½ QV
Dielectric Strength (oops I burned it/broke it)
Capacitor Enhancement by inserting a
dielectric:
Replace εo by κεo
PHY 2049: Physics II
PHY 2049: Physics II
1
1
1
1
=
+
+
C eq C1 C2 C3
Ceq = C1+C2+C3
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5/18/2011
PHY 2049: Physics II
PHY 2049: Physics II
Charging and discharging of capacitors.
http://edugen.wiley.com/edugen/instructor/
main.uni
25.20
PHY 2049: Physics II
PHY 2049: Physics II
Switch closed on left, capacitor C1 is being
charged
Q1 = C1V =10µ ×10V =100µC
We have C2 = C3 = 20 µF in parallel.
The equivalent capacitor is then Ceq = 40
µF. When the switch is thrown to right,
the battery is disconnected, the charge is
shared between the capacitors C1 and
Ceq = 40. What is the charge on old C2
and C3? Is your answer 40 µC? What is
your answer if C2 = 10 µF and C3 = 30
µF?
V1 =Veq
Q1' Qeq
= ⇔Q1'+Qeq =100µC
C1 Ceq
Q1' = 20µC,
V1' = 2Volts
Qeq = 80µC,
Veq= 2Volts.
All about capacitors
Capacitance units Farad
C = 4 π κεo R for a sphere of radius R and
dielectric constant κ.
Energy stored dielectrics and strength
Parallel and series elements in a network
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