potential difference

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Transcript potential difference

Potential Difference
Electric Potential
Gravitational potential energy

20 Jkg-1



2m

1m
2kg
1kg

How much energy is needed
to lift 1kg onto the table?
PE = mgh = 10J
How much energy does it
take to lift 2kg onto the
table?
20J
Masses on the table possess
10 joules per kilogram
What is the potential
difference between the top of
the stool and the floor?
Electrical Potential Difference
B
100 V
+
+
+
+

-

-
++
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-
+
+
A
++
+
+
-

-


E = QV


1 volt = 1 joule per coulomb
The potential difference
between these two plates is
100 volts = 100 JC-1
How much energy is required
to move 1 coulomb from A to
B?
100J
How much energy for 2 C?
E = qV = 2 x 100 = 200J
And 3 C?
300J
Question
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The potential difference between the dome
of a Van de Graaff generator and earth is
100 000 V. How much energy is released
when a spark containing 0.5μC of charge
discharges to earth?
E = QV
= 5 x 10-7 x 1 x 105
= 0.05 J
1 electron volt is the
energy needed to move 1
electron through a
potential difference of I
volt
 1 joule of energy
Electron Volt
B
A
1V
+
+
-
+
+

-
e-
coulombs

volts

joules
Electron
volts
E = Qv
electrons

volts
is the
energy needed to move 1
coulomb through a potential
difference of 1 volt.
How much energy is
needed to move 1 electron
through a potential
difference of 1 volt
The charge on 1 electron is
1.6 x10-19 C
E = QV = 1.6 x 10-19 x 1
= 1.6 x 10-19J
This is called 1 electron volt
Electric Potential
The
potential at a point is
the amount of work needed
to move a unit positive
charge from infinity to that
point (unit J/C)
+



The potential around a
point charge is given
by the equation V =kq/r
Where is potential
zero?
At infinity
V = kq/r
+
V=0
Potential due to Point Charge

V = kQ/r
V = kq/r
+
V=0
-
Potential changes
suddenly because field
is strong (steep slope)
Potential changes
gradually because field
is weak (gentle slope)
Negative potential
so work is needed
to get the charge
back to infinity
+
+
More than one charge
V = kq/r + kq/r
= 2kq/r
r
V = kq/r - kq/r
Potential is a
scalar quantity
=0
r
r
+q
+q
r
+q
-q
Work is done
against repulsive
forces from both
charges
+
Work is done
against the positive
charge and by the
negative charge
+
E = ΔV/Δx
B
100 V
+
+
+q
A

-

-
+
-

+
-

+
-
+
-

ΔW = qΔV
ΔW = FΔx
FΔx = qΔV
F/q = ΔV/Δx
E = ΔV/Δx
E = ΔV/Δx
100 V
100 V
+
-
+
-
+
+q
+
-
+
-
+
-
+
-
+
-
+
-
-
+
+
-
+
-
+
-
+
-
+
+q
ΔV
ΔV
m
m
Δx
Δx
+q
ΔV
-
m
Δx
The charge
gains
energy
The
charge
gainsis
The distance
as
it moves
a
the
same
amount
the same but
distance
of energy
in aΔX
the energy
shorter
 The distance.
steepness
gained
is less
This
means
the
of
the
slope
so the
field
has field
to be must
represents the
stronger
be less strong
field strength

50 V
Just like gravitation
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F = G Mm/r2
g = F/m = GM/r2
the units of g are Nkg-1
The potential at a point is
the work done to move a
unit mass from infinity to
that point
V = -GM/r
Units of V are JKg-1

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F = Kq1q2/r2
E = F/q = kq/r2
the units of E are NC-1
The potential at a point is
the work done to move a
unit charge from infinity to
that point
V = kq/r
Units of V are JC-1
Equipotentiallines
and field lines
always cross at 90
degrees
Equipotentials

+
+
+
-

Equipotentials
are lines
joining points
with the same
potential.
They are a bit
like contour
lines on a
map
Field lines point from high potential to low potential. They are like
lines pointing downhill on a map