PHY 2054: Physics II
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HITT, please contact and inform in case of
problems
Hopefully all webassign problems have been
solved. Please see me immediately after
the class if there is still an issue.
SI for T6 meeting, the room has been
changed from MCCB 2102. New room MCCB
3108
PHY 2054: Physics II
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Some effects of potentials and potential
energy.
Parallel and Series configurations for
capacitors.
HITT I
An ion is released from rest and moves due
to the force from an electric field from a
position in the field having a potential of 14 V
to a position having a potential of 8 V. The
ion:
a. must have a positive charge.
b. must have a negative charge.
c. can have either a positive or a negative
charge.
d. must be neutral.
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Some old business:
What is the electric field
of a shell
of a uniform spherical charge distribution?
What is the potential for each of the above?
The story of the integration constant.
PHY 2054: Physics II
kq
r > R2
Er = 2
r
3
kq r 3 − R1
= 2 3
r R2 − R13
=0
R1 < r < R2
r < R1
r
V (r ) = − ∫ E.dr
∞
V(∞) = 0
This one takes effort but can be done.
kq
Er = 2
r
kq
= 3r
R
r>R
r<R
r
kq
V (r ) − V (∞) = − ∫ E.dr =
r
∞
2
⎡
kq
⎛r⎞ ⎤
=
⎢3 − ⎜ ⎟ ⎥
2 R ⎢⎣ ⎝ R ⎠ ⎥⎦
r>R
PHY 2054: Physics II
Options:
E
R
V
V
r
„
V(∞) = 0
„
V (0) = 0
PHY 2054: Physics II
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q1= q, q2 = -4q, q3 = +2q
d=.12 , q = 150 nC
The system has to be held.
If let go, would it implode or
fly apart.
PHY 2054: Physics II
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q1= q, q2 = -4q, q3 = +2q
d=.12 , q = 150 nC
The system has to be held.
If let go, would it implode or
fly apart.
The potential energy
= - 10kq2/d
it implodes
HITT II
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An electron with velocity v = 1.0
× 106 m/s is sent between the
plates of a capacitor where the
electric field is E = 500 V/m. If
the distance the electron travels
through the field is 1.0 cm, how
far is it deviated (Y) in its path
when it emerges from the electric
field? (me = 9.1 × 10−31 kg, e =
1.6 × 10−19 C)
a. 2.2 mm
b. 4.4 mm
c. 2.2 cm
d. 4.4 cm
1 cm
v
Y
PHY 2054: Physics II
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q = CV
C = εoA/d
1F = 1Coulomb/Volt
PHY 2054: Physics II
2kq
E=
Lr
b
2kq q
V (a ) − V (b) = ∫ dr
=
Lr C
a
L
C = 2πε 0
ln b
( a)
PHY 2054: Physics II
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In Parallel
Total charge
q = q1 + q2 + q3
=(C1 + C2 + C3 )V
C = C1 + C2 + C3
PHY 2054: Physics II
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Series: the charges
are same, potentials
add.
V = V1 + V2 + V3
1 1
1
1
=
+
+
C C1 C2 C3
PHY 2054: Physics II
1
1
1
=
+
C C3 C1 + C2
HITT III
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What is the equivalent
capacitance between
points a and b? All
capacitors are 1.0 μF.
a. 4.0 µF b. 1 7 µF
c. 0.60 µF d. 0.25 µF
a
b
PHY 2054: Physics II
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Potentials are always measured in
difference. This avoids the choice of the
integration constant.
Capacitors are charge holders. Their ability
to hold charge is measured by C. Their
true “capacity” is called breakdown
strength.
C = εox length, Thus 10 cm leads to 1 pF.
PHY 2054: Physics II
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About bicycle riding: If some one shows
you a trick, it means that,
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It is possible to do that trick
The person who showed you, can do the trick.
It does not mean that you can do the trick.
Try it a lot of times and you can too.
PHY 2054: Physics II
dq = σ (2πR')dR '
dq
dV = k
= k σ (2π2R ' )dR2 '
R' + z
r
σ
=
2ε o
(z
2
+R −z
2
)
z
σ ⎛
∂V
⎜1 −
Ez = −
=
2
2
∂z 2ε o ⎜⎝
z +R
⎞
⎟
⎟
⎠
PHY 2054: Physics II
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Gold, 79p,118n
α : 2p,2n
Approach = 9.23
x 10-15 m
Initial kinetic
energy = 24.6
MeV
PHY 2054: Physics II
λdx
dq
= k∫
V =k
2
2
r
+
x
d
0
L
[(
(
= kλ ln x + x + d
2
2
)
1/ 2
)]
L
0
⎡ L + L2 + d 2 ⎤
= kλ ln ⎢
⎥
d
⎢⎣
⎥⎦
What happens if the point P is not at the end of the
wire.