Download PHYS_3342_092211

Our first exam is next Tuesday - Sep 27. It will cover everything I have covered in
class including material covered today.
There will be two review sessions Monday, Sep 26 - at 12:30 PM and at 3:00 PM in
the same room as the problem solving session: FN 2.212.
I have put several (37) review questions/problems on Mastering Physics. These are
not for credit but for practice. I will review them at the review session Monday.
Example: A positively charged (+q) metal sphere of radius ra is inside
of another metal sphere (-q) of radius rb. Find potential at different points
inside and outside of the sphere.
a) r  ra : b)ra  r  rb : c)r  rb
1
-q
a)
2
V2 (r ) 
V1 (r ) 
+q
q
4 0rb
q
4 0ra
Total V=V1+V2
b)
Electric field between spheres
q 1 1
V (r ) 
  
4 0  r rb 

E
r
V (r ) 
c)
q 1 1
  
4 0  ra rb 
V 0
Equipotential Surfaces
• Equipotential surface—A surface consisting of a continuous
distribution of points having the same electric potential
• Equipotential surfaces and the E field lines are always
perpendicular to each other
• No work is done moving charges along an equipotential surface
– For a uniform E field the equipotential surfaces are planes
– For a point charge the equipotential surfaces are spheres
Equipotential Surfaces
Potentials at different points are visualized
by equipotential surfaces (just like E-field
lines).
Just like topographic lines (lines of equal
elevations).
E-field lines and equipotential surfaces are
mutually perpendicular
Definitions cont
• Electric circuit—a path through which charge can flow
• Battery—device maintaining a potential difference V
between its terminals by means of an internal
electrochemical reaction.
• Terminals—points at which charge can enter or leave a
battery
Definitions
• Voltage—potential difference between two points in space (or a
circuit)
• Capacitor—device to store energy as potential energy in an E
field
• Capacitance—the charge on the plates of a capacitor divided by
the potential difference of the plates C = q/V
• Farad—unit of capacitance, 1F = 1 C/V. This is a very large unit
of capacitance, in practice we use F (10-6) or pF (10-12)
Capacitors
• A capacitor consists of two conductors called plates which get equal
but opposite charges on them
• The capacitance of a capacitor C = q/V is a constant of
proportionality between q and V and is totally independent of q and
V
• The capacitance just depends on the geometry of the capacitor, not q
and V
• To charge a capacitor, it is placed in an electric circuit with a source
of potential difference or a battery
CAPACITANCE AND CAPACITORS
Capacitor: two conductors separated by
insulator and charged by opposite and
equal charges (one of the conductors can be
at infinity)
Used to store charge and electrostatic
energy
Superposition / Linearity: Fields, potentials and potential
differences, or voltages (V), are proportional to charge
magnitudes (Q)
C
Q
V
(all taken positive, V-voltage between plates)
Capacitance C (1 Farad = 1 Coulomb / 1 Volt) is
determined by pure geometry (and insulator properties)
1 Farad IS very BIG: Earth’s C < 1 mF
Calculating Capacitance
1.
2.
Put a charge q on the plates
Find E by Gauss’s law, use a surface such that
 
qenc
 E  dA  EA 
0
3.
Find V by (use a line such that V = Es)
 
V   E  ds  Es
4.
Find C by
q
C
V
Parallel plate capacitor
Energy stored in a capacitor is related to the E-field between the plates
Electric energy can be regarded as stored in the field itself.
This further suggests that E-field is the separate entity that may exist alongside
charges.
density   charge Q /area S

Q
Qd
E 
; V  Ed 
0 0 A
0 A
A
C 0
d
Generally, we find the potential difference
Vab between conductors for a certain
charge Q
Point charge potential difference ~ Q
This is generally true for all capacitances
Capacitance configurations
Cylindrical capacitor
Spherical Capacitance
b
dr
1 1
V  k e Q  2  ke Q(  )
ra rb
a r
b
dr
Q b
V  2ke    2ke ln( )
r
l
a
a
C
l
b
2ke ln( )
a
ra rb
C
k e (rb  ra )
With rb , C  ra /k e capacitance of an individual sphere
Definitions
• Equivalent Capacitor—a single capacitor that has the same
capacitance as a combination of capacitors.
• Parallel Circuit—a circuit in which a potential difference applied
across a combination of circuit elements results in the potential
difference being applied across each element.
• Series Circuit—a circuit in which a potential difference applied
across a combination of circuit elements is the sum of the
resulting potential differences across each element.
Capacitors in Series
Q
Q
Vac  V1  ; Vcb  V2 
C1
C2
Total voltage
V  V1  V2
Equivalent
1 V
1
1
 

C Q C1 C2
Capacitors in Parallel
Total charge
Q  Q1  Q2
Equivalent
C
Q
 C1  C2
V
Example: Voltage before and after
Initially capacitors are charged by
the same voltage but of opposite polarity :
Q1i  C1Vi ; Q2i  C2Vi
Total charge Q  Q1i  Q2i  Q1 f  Q2 f
Equivalent
C  C1  C2
Voltage after : V f 
Q C1  C2

Vi
C C1  C2