PHY 2049: Physics II



Coulomb’s law,
electric field, Gauss’
theorem and electric
potential.
-W = qΔV
Energy conservation
applies.
F
U
U
F 
x
F  qE
E
U  qV
V
E
x
V
PHY 2049: Class Quiz
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
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
Calculate the Electric Field at P
Calculate the el. potential at P
2kq 
1 
E x  2 51 

d  2 2
2kq 3
Ey  2
d 2 2
kq
V  4
d
PHY 2049: Physics II
•Point charge
q
V k
r
•Distribution of charges
qi
 k
i ri
•Line charge at an edge
l  l 2  d 2 
 k ln 

d


•Disc on an axis through
the center


( z 2  R 2  z)
2 o
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?
PHY 2049: Physics II

E
R
V
r
The potential of a
uniform spherical
charge.

V
Some old business
Calculate electric
field, integrate it to
get the potential






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
PHY 2049: Physics





a= 39 cm
q1 = 3.4pC
q2 = 6 pC
E at the center?
What is the
potential at the
center?
k
V  8q 2
a
II E  1.6 kq21 ,
a
26.6
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.
PHY 2049: Physics II
PHY 2049: Physics II

V  Ed 
d
o
C  o
A
d
Potential near a sheet charge
V ( z )    E.dz  Const

 V 
z
2 o
Potential near a sheet charge
V ( z )    E.dz  Const

 V  z
o
Q
V  V 
d
o A
C  o A / d
PHY 2049: Physics II
PHY 2049: Physics II
 1
E (r )  
2o r
V r     E.dr


ln r
2o
Q
b
Va  Vb 
ln
2o h a
C  2o h ln( b / a)
PHY 2049: Physics II
q
Ek 2
r
q
V r   k
r
1 1
Va  Vb  kq  
a b
 ab 
C  4o 
  4o R
ba
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?
a. 400 V
d. 2500 V
b. 1600 V
c. 2200 V
PHY 2049: Physics II

What is the capacitance of various familiar
balls.
C = 4πεoR = 10-10 R(m) F



Basketball-it is an insulator
Van de Graff top
Earth (radius 6.4 X 106 m)

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
Ceq = C1+C2+C3
PHY 2049: Physics II
1
1
1
1
 

C eq C1 C2 C3
PHY 2049: Physics II


Charging and discharging of capacitors.
http://edugen.wiley.com/edugen/instructor/
main.uni
PHY 2049: Physics II
25.20
PHY 2049: Physics II
Switch closed on left, capacitor C1 is being
charged
Q1  C1V  10 10V  100C
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  100 C
C1 Ceq
Q1 '  20C ,
V1 '  2Volts
Qeq  80C ,
V eq 2Volts.
PHY 2049: Physics II





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