CHAPTER   23
ELECTRIC   POTENTIAL
BASIC   CONCEPTS:
ELECTRIC   POTENTIAL   ENERGY
ELECTRIC   POTENTIAL
ELECTRIC   POTENTIAL   GRADIENT   –
POTENTIAL   DIFFERENCE
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POTENTIAL   ENERGY
h
PE   =   U   =   mgh
PE         KE
Or
U          K
And   U   +   K   =   total   energy   =   constant
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BOOK   EXAMPLE
3

Charged   Particle   in   Electric   Field   is   similar
4

Consider   a   point   charge   q   that   sets   up   an   electric   field   in   space
5

Now   a   test   charge   q
0
is   placed   at   position   a   a   distance   r a
from   q
0 .
Then    q
0
moves   to   position   b   a   distance   r b
from   q
0
.
What   is   the   change   in   potential   energy?
The   change   in   potential   energy   is   the   negative   of   the   work   done   to   move   the   test   charge   from   a   to   b .
The   force   on   the   test   charge   is
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The   work   done   is   force   times   distance.
But   the   force   changes   as   q
0
moves   away   from   q
Must   integrate
Use
Then
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The   change   in   potential   energy,   is   the   negative   of   this   work.
DEFINITION:
ELECTRICAL   POTENTIAL   IS   POTENTIAL
ENERGY   PER   UNIT   CHARGE
8

Therefore   divide   all   terms   by
Thus
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Now   consider   the   same   situation
10

We   have   as   we   did   at   the   beginning
The   change   in   potential   energy,   is   the   negative   of   this   work.
Therefore
In   Chapter   21   we   defined   the   Electric   Field   as   the   force   per   unit   charge
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And   we   have
Divide   all   terms   by   q
0
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POTENTIAL   AT   A   POINT
Once   again   look   at   this   situation
We   have
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Just   like   in   potential   energy   of   the   particle   on   a   hill   we   can   choose   the   potential   energy   and   therefore   the   potential   to   be   zero   at   any   arbitrary   point.
Choose   infinity
In   the   figure
When
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Then
From   Chapter   21
Therefore
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Choose            where
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The   potential   at   any   point   in   space   a   distance   from   a   charge     will   be
POTENTIALS   ADD   (SCALERS)
Just   as   we   did   with   the   electric   field   we   can   add   the   potentials   for   many   charges   in   an   area.
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EXAMPLE
A
60cm
30cm
50µC                            ‐ 50   µC
What   is   the   potential   at   A?
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Example   23.11
Potential   on   axis   of   ring   of   charge.
Choose   small   segment   of   ring     that   has   charge   .
The   segment   is   a   distance     form   point   P.
Then
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Integrate   to   get   V
Everything   is   constant   except
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Use   the   result   to   find   potential   on   axis   of   disk   of   charge.
This   is   diagram   for   E   but   use   it   for   finding   potential   at   P
For   ring   of   radius     contribution   to   V   is
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Disk   is   made   up   of   rings   each   with   area
Charge   density   of   disk   is   total   charge     divided   by   total   area
Therefore
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Integrate
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For   the   disk
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TWO   MORE   BASIC   PIECES   OF   INFORMATION
If   we   know   V   we   can   find   E
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Example
In   this   chapter   we   found   for   ring   of   charge
In   chapter   21   we   found   for   ring   of   charge
Use   equation   above   for   V   to   find
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ELECTRON   VOLT
An   electron   volt   is   a   unit   for   energy.
It   is   the   work   necessary   to   move   an   electron
(charge   difference   of   1   volt.
)   a   potential
1   Volt   Batt
The   work   to   move   a   charge     across   a   potential   difference   is
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Therefore
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