Lecture11 - Announcement:


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Unformatted text preview: Announcement:
 
Exam
1:
9/30



Thursday
9:00
am‐10:20
am
 




































Half
of
exam
will
be
done
on
scantron
 
 
 
 
 
[show
an
example
scantron
sheet
on
doc
cam]
 




































2~3
wriEen
quesGons
 








Extra
review
session:
9/27
7
to
9
pm
MAP
318
[conference
room]
 




Unregistered
clickers
will
be
posted
on
the
website
 physics.ucf.edu/~ishigami/Teaching/fall102049/physics20492010Fall.html
 Scantron
form
to
be
used
 hEp://www.ucfsga.com/?p=scantrons
 Examples
of
PotenGal
CalculaGon
 Uniformly
Charged
Sphere
with
radius
a

 r a
 P
 Electric
field
outside
:



Gaussian
surface
is
spherical
shell
with
radius
r
 Qenclosed = Q r
 a
 Φtotal = E ⋅ ndS = E ⋅ A = 4π r 2 E ∫ˆ Qenclosed = ε0 Φtotal Q 4π r E = ε0 2 1Q E (r ) = 4πε 0 r 2 E
inside
 Qenclosed a
 43 πr r3 =Q 3 =Q 3 43 a πa 3 Φtotal = E ⋅ ndS = E ⋅ A = 4π r 2 E ∫ˆ r
 Φtotal Qenclosed = ε0 r3 Q3 4π r 2 E = a ε0 1 Qr E (r ) = 4πε 0 a 3 Uniformly
Charged
Sphere
with
radius
a

 r a
 P
 Outside
(r
>
a)
 Inside
(r
>
a)
 1Q E (r ) = 4πε 0 r 2 1 Qr E (r ) = 4πε 0 a 3 E = −∇V dV ˆ E=− r dr V (r ) = − ∫ E (r ) dr V (∞ ) = 0 Uniformly
Charged
Sphere
with
radius
a:
potenGal
outside
(r
>
a)

 r a
 P
 1Q E (r ) = 4πε 0 r 2 V (r ) = − ∫ E (r ) dr V (∞ ) = 0 1Q 1Q V (r ) = − ∫ dr = + Cons tan t 2 4πε 0 r 4πε 0 r Cons tan t = 0 V (r ) = 1Q 4πε 0 r Uniformly
Charged
Sphere
with
radius
a:
PotenGal
Inside
r
<
a

 r a
 P
 1 Qr E (r ) = 4πε 0 a 3 V (r ) = − ∫ E (r ) dr 1Q V (a ) = 4πε 0 a 1 Qr 1 Qr 2 V (r ) = − ∫ dr = − + Cons tan t 3 3 4πε 0 a 8πε 0 a 1Q 1 Qa 2 V (a ) = =− + Cons tan t 3 4πε 0 a 8πε 0 a 1Q 1Q 1 3Q Cons tan t = + = 4πε 0 a 8πε 0 a 4πε 0 2 a Example:
ConducGng
Sphere
with
total
charge
Q
 r a
 P
 1 V (r ) = 4πε 0 1 V (r ) = 4πε 0 Q ,r > a r Q ,r < a a What
about
a
non‐tradiGonal
objects?
 ConducGng
irregular
shaped
object
 Radius
b
 Radius
a
 Capacitance
 Q C= ΔV Units:
Farads
(Coulomb
per
Volt)
 Example
1:
Parallel
Plate
Capacitor
 Area:
A
 d
 Calculate
the
capacitance
of
parallel
plate
capacitor
 Area:
A
 +Q
 d
 ‐Q
 1.  Put
equal
and
opposite
charge
on
each
plate
(imagine)
 2.  Calculate
the
voltage
difference
between
the
plates
 3.  Apply

 C= Q ΔV Proceed
on
Blackboard
 Spherical
capacitor
 b
 a
 Example:
ConducGng
sphere
with
charge
Q
and
radius
a
 a
 1Q V (a ) = 4πε 0 a Q = CV (a ) C = 4πε 0 a ...
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This note was uploaded on 07/16/2011 for the course PHY 2049 taught by Professor Saha during the Fall '08 term at University of Central Florida.

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