Physics 2220 Chapter 24 Electric Potential

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Physics 2220Chapter 24 Electric Potential

• Quiz Using Gausss Law determine the electric
  field E inside and outside of a thin spherical
  shell that carries a uniform surface charge s of
  radius a.

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Physics 2220Chapter 24 Electric Potential

• Quiz Using Gausss Law determine the electric
  field E inside and outside of a thin spherical
  shell that carries a uniform surface charge s of
  radius a.

Inside ER (4pr 2) q/eo 0 ? ER 0.
r
r
a
Outside ER (4pr 2) q/eo ? ER (4pa 2)s/
eo(4pr 2) ER a 2s/ eor 2
s
N.B. at r a, outside ER s/ eo , sheet
charge result
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Physics 2220Chapter 24 Electric Potential

• 1' Lesson
• The Electric Potential is the Potential Energy
  per unit test charge due to the electric field of
  a distribution of charges.
• ?V ?UE/qo

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Physics 2220Chapter 24 Electric Potential

• Electric Potential vs Potential Energy

?UE - ?FE ?d s - qo ?E ?d s
?V ?UE /qo
?V - ? E ?d s
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Physics 2220Chapter 24 Electric Potential

• Unit of Potential, Volt

Electric Field
V J/C
N/C V/m
Volt
Joule/ Coulomb
Joule / Coulomb
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Physics 2220Chapter 24 Electric Potential

• Potential Near a Sheet of Charge

E êz Ez êz s / 2eo
?UE - qo ?E ?d s
?UE - qo ?Ez d z
?UE - qoEz ?z
?V ?UE /qo
?V - Ez ?z ?V - s ?z / 2eo
s
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Physics 2220Chapter 24 Electric Potential

• Application and Practice (AP)
• What is the electric field between two parallel
  plates attached to the terminals of a 12 V
  battery, if the plates are very large and the
  separation is 3.00 mm?

V 0
E V/d 12 V/(.003 m)
E 4000 V/m
V 12 V
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Physics 2220Chapter 24 Electric Potential

• Potential due to Point Charge q
• ?V - ? E ?d s
• ?V - ?8 R keq/r 2dr
• ?V keq / R

Equipotentials
V
R
R
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Physics 2220Chapter 24 Electric Potential

• Equipotential Lines
• Equipotential lines are lines that connect
  positions of equal electric potential.
• For example a sheet of charge

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Physics 2220Chapter 24 Electric Potential

• Superposition Principle for V
• V Si1Vi
• V ke Si1 qi /ri
• V ke ? dq /r

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Physics 2220Chapter 24 Electric Potential

• Electric Potential of a Dipole

q
r
V ke q /r-ke q/r-
r
?
2a
V ke q (r- -r)/rr-
r-
-q
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Physics 2220Chapter 24 Electric Potential

• Equipotential Potential of a Dipole

q
V 2a keq cos ?/r 2 constant
r
r
2a
Requipot v 2a keq cos ?/V
r-
-q
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Physics 2220Chapter 24 Electric Potential

• Electric Field from the Electric Potential
• Ex -?V/?x

Ey -?V/?y
Ez -?V/?z
E - êx ?V/?x - êy ?V/?y- êz ?V/?z
E - ?V
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Physics 2220Chapter 24 Electric Potential

• Electric Field of Dipole from the Potential

q
V 2a keq cos ?/r 2 p cos ?/r 2
r
Er -?V/?r 2pcos ?/r 3 E? -?V/r? ? psin
?/r 3
r
2a
r-
-q
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Physics 2220Chapter 24 Electric Potential

• Summary

• ?UE - ?FE ?d s - qo ?E ?d s
• ?V ?UE / qo - ? E ?d s
• ?V - E d for uniform E
• ?V keq / R for point charge
• V ke ? dq /r for distribution of charge
• Ex -?V/?x

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Physics 2220Chapter 24 Electric Potential
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Physics 2220Chapter 24 Gausss Law

• Applications of Gausss Law
• A spherically symmetric charge density ?

ER (4pR2 ) (1/eo )?? dV
?
ER 1/(4 peoR2 )?? dV
ER
R
dA
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Physics 2220Chapter 24 Gausss Law

• Applications of Gausss Law
• A spherically symmetric charge density ?

ER (4pR2 ) (1/eo )?? dV
?
ER 1/(4 peoR2 )?? dV
R
ER q/(4 peoR2 ) Rgta
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Physics 2220Chapter 24 Gausss Law

• Summary
• FE ?S E?dA Electric Flux
• ? E?dA q/eo Gausss Law
• Ez s / eo E outside conducting plate E 0
  inside conductor
• Ez s / 2eo E for infinite sheet of s
• ER q/(4 peoR2 ) E outside spherical q
• ER ?/(2peo R) E for line charge of ?

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Physics 2220Chapter 24 Gausss Law

• Application and Practice
• Calculate the electric potential at a distance R
  from an infinite line of charge with a uniform
  charge density ?.(Assume V0 _at_ R 1.

V ke ? dq /r ke ? ? dz /r 2ke ?08 ? dz
/z2 R21/2 2ke ? ln (z v z2 R2 )08 2ke
? ln R
z
R
?
r
dz
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Physics 2220Chapter 24 Electric Potential