lecture 6-1 please read the textbook before each lecture and come to the lecture with questions the...
DESCRIPTION
Lecture 6-3 Electrostatic Shielding (Continued) Add Q’ If you now add charge Q’ to the conductor and/or Q’’ on the outside of the conductor, the interior electric fields do not change. Q’’ If you move charge q in the cavity, the exterior electric fields and the extreior charge distribution are not affected. Conducting shell electrostatically shields its exterior from changes on the inside. q Conducting shell electrostatically shields its interior from changes on the outside, too.TRANSCRIPT
Lecture 6-Lecture 6-11
Please read the textbook before each Lecture and
Come to the lecture with questions
The chapter to be covered is at the end of the syllabus
Lecture 6-Lecture 6-22Thin sheet of any charge distribution
'R diskE E E 'L diskE E E
Just to left of disk
Just to right of disk
0 0
0
( ' )
( ' )
2 2
disk
disk
disk disk
E E E
E E
E E
n
n
tiny disk
0nE
Lecture 6-Lecture 6-33 Electrostatic Shielding (Continued)
++++
+
+
Add Q’ If you now add charge Q’ to the conductor and/or Q’’ on the outside of the conductor, the interior electric fields do not change.
Q’’
If you move charge q in the cavity, the exterior electric fields and the extreior charge distribution are not affected.
Conducting shell electrostatically shields its exterior from changes on the inside.
q
Conducting shell electrostatically shields its interior from changes on the outside, too.
Lecture 6-Lecture 6-44Gravitational vs Electrostatic Potential Energy
( ) ( )b
a
U U b U a
dF l
a
bqE
mg
Gravity Coulomb
b
aldF
b
a
Lecture 6-Lecture 6-55Electric Potential Energy of a Charge (continued)
i is “the” reference point. Choice of reference point (or point of zero potential energy) is arbitrary.
0
dl
i is often chosen to be infinitely far ( )
0
( ) ( )r
i
U U r U i
q E dl
r
ildEq0
Lecture 6-Lecture 6-66Potential Energy in the Field due to a Point Charge q
0
02
02
0 0
( )P
P
r
r
U r q E dl
q qk r dl
lq qk dll
q q q qk k
l r
From ∞
This is also called the potential energy of the two-charge configuration of q and q0.
P
ldEq0
Lecture 6-Lecture 6-77Potential Energy of a Multiple-Charge Configuration
1 2 /kq q d
1 31 32 2
2q q qq qk k k
ddq
d
dqqk
dqqk
dqqk
dqqk
dqqk
dqqk
22413243423121
Lecture 6-Lecture 6-88Physics 241 –Warm-up quiz
Three point charges carry the same charge -q. Which of the following statements is true? Select one of (a) – (e).
A. An electron would have a higher potential energy at point A than at point B
B. A proton would have a higher potential energy at point A than at point B
C. An electron would have a lower potential energy at point A than at point B
D. The potential energy is the same for an electron and a proton at point A.
E. The potential energy is the same for a proton at point A and point B.
A B-q-q
-q
Lecture 6-Lecture 6-99Electric Potential
• So U(r)/q0 is independent of q0, allowing us to introduce electric potential V independent of q0.
0
( )( ) U rV rq
• U(r) of a test charge q0 in electric field generated by other source charges is proportional to q0 .
0
( )( ) U rV rq
taking the same reference point
rr
ldEqldEqrV 00)(
Lecture 6-Lecture 6-1010Potential at P due to a point charge q
0
0
( )( ) qU r
V rqqkr
From ∞
V(r) drop following the direction of electrical field.
Lecture 6-Lecture 6-1111Electron Volt
• V=U/q is measured in volts => 1 V (volt) = 1 J / 1 C
J N mV E m VC CN VEC m
19
1 1 1
1 | | 1 1.602 10 1
J C V
eV e V C V
• V depends on an arbitrary choice of the reference point.• V is independent of a test charge with which to measure it.
(electron volt)
Potential energy difference when 1 C of charge is moved between points of potential difference 1 V
Lecture 6-Lecture 6-1212Potential due to two (source) charges
1 2( )| | | |q qV x k kx x a
1 2 0q q
Lecture 6-Lecture 6-1313Potential due to Multiple Source Charges: Example
1 2 3 4
( )
/ 2
V Pq q q qk
d
Dotted line is an equipotential when
q1=12nC, q2= -24nC, q3=31nC, q4=17nC
E from V
xVEx
yVEy
z
VEz
Expressed as a vector, E is the negative gradient of V
VE
We can obtain the electric field E from the potential V by inverting the integral that computes V from E:
r
zyx
r
dzEdyEdxEldErV )()(
Lecture 6-Lecture 6-1515 Lightning
E = 3 x 106 N/C
at electrical breakdown of air
V on the order of 109 V
http://micro.magnet.fsu.edu/electromag/java/lightning/index.html
Examples (only a Preview)
Point charge Q: ( ) QV r kr
2( ) Q VE r k r r
r r
Charged disk: ( ) ??V z 2 2
0
( ) (1 )2
V zE z z zz z R
( ) QV r kr
2( ) QE r k rr
Uniformly charged sphere:
r > R
r < R2
20
1( ) 34 2
Q rV rR R
30
1( )4
QrE r rR
Charged sheet:0
( ) sgn( )2
E z z z
( ) ??V z
Charged line: ( ) ??V z 0
( )2
E r rr
Lecture 6-Lecture 6-1717Physics 241 –Quiz 4a
A spherical shell is uniformly charged with a positive charge density . Which of the following statements is (are) true? Select one of (a) – (e).
1. An electron would have a higher potential energy at point A than at point B
2. A proton would have a higher potential energy at point A than at point B
3. The electric potential is lower at A than at B 4. The electric potential is higher at A than at B
A B
a) 1 and 3 onlyb) 1 and 4 onlyc) 2 and 3 onlyd) 2 and 4 onlye) None of them
Lecture 6-Lecture 6-1818Physics 241 –Quiz 4b
A plane is uniformly charged with a positive charge density . Which of the following statements is (are) true? Select one of (a) – (e).
1. A proton would have a higher potential energy at point A than at point B
2. An electron would have a higher potential energy at point A than at point B
3. The electric potential is lower at A than at B 4. The electric potential is higher at A than at B
A B
a) 1 and 3 onlyb) 1 and 4 onlyc) 2 and 3 onlyd) 2 and 4 onlye) None of them
Lecture 6-Lecture 6-1919Physics 241 –Quiz 4c
A sphere is uniformly charged with a negative surface charge density . Which of the following statements is (are) true? Select one of (a) – (e).
1. A proton would have a higher potential energy at point A than at point B
2. An electron would have a higher potential energy at point A than at point B
3. The electric potential is lower at A than at B 4. The electric potential is higher at A than at B
A B
a) 1 and 3 onlyb) 1 and 4 onlyc) 2 and 3 onlyd) 2 and 4 onlye) None of them