Transcript electric potential difference

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Topic 9.3
Electric Field, potential
and Energy
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Electric Potential Energy
 If
you want to move a charge closer to a charged
sphere you have to push against the repulsive force
 You do work and the charge gains electric
potential energy.
 If you let go of the charge it will move away from
the sphere, losing electric potential energy, but
gaining kinetic energy.
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When
you move a charge in an
electric field its potential energy
changes.
This is like moving a mass in a
gravitational field.
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 The
electric potential V at any point in an
electric field is the potential energy that each
coulomb of positive charge would have if
placed at that point in the field.
 The unit for electric potential is the joule per
coulomb (J C-1), or the volt (V).
 Like gravitational potential it is a scalar
quantity.
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In the next figure, a charge +q moves between points
A and B through a distance x in a uniform electric
field.
 The positive plate has a high potential and the
negative plate a low potential.
 Positive charges of their own accord, move from a
place of high electric potential to a place of low
electric potential.
 Electrons move the other way, from low potential to
high potential.

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 In
moving from point A to point B in the
diagram, the positive charge +q is moving
from a low electric potential to a high
electric potential.
 The electric potential is therefore different
at both points.
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 In
order to move a charge from point A to point B,
a force must be applied to the charge equal to qE
(F = qE).
 force is applied through a distance x, then work
has to be done to move the charge, and there is an
electric potential difference between the two
points.
 work done is equivalent to the energy gained or
lost in moving the charge through the electric field.
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If a charge moves at an angle θ to an electric field, the component of the
displacement parallel to the electric field is used as shown in the next
figure.
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Electric Potential Difference
Potential difference
What is difference in potential between two
points in an electric field
The potential difference or p.d. is the energy
transferred when one coulomb of charge
passes from one point to the other point.
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The diagram shows some values of the electric potential at points
in the electric field of a positively-charged sphere
What is the p.d. between points A and B in the diagram?
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Change in Energy
Energy transferred,
This could be equal to the amount of electric
potential energy gained or to the amount of
kinetic energy gained
W
= charge (q) x p.d.(V)
(joules) (coulombs) (volts)
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The Electronvolt
One electron volt (1 eV) is defined as the energy
acquired by an electron as a result of moving
through a potential difference of one volt.
W=qxV
charge on an electron or proton is
1.6 x 10-19C
Then W = 1.6 x 10-19C x 1V
W
= 1.6 x 10-19 J
Therefore 1 eV = 1.6 x 10-19 J
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Electric Potential due to a Point Charge
The electric potential at a point in an electric field is
defined as being numerically equal to the work
done in bringing a unit positive charge from
infinity to the point.
Electric potential is a scalar quantity and it has
the volt V as its unit.
Based on this definition, the potential at infinity is
zero.
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
Consider a point r metres from a charged object. The potential at
this point can be calculated using the following
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Electric Field Strength and Potential
Suppose that the charge
+q is moved a small
distance by a force F
from A to B so that the
force can be
considered constant.
What is the work done?
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The work done is given by:
ΔW = Fx Δx
The force F and the electric field E are oppositely
directed, and we know that:
F = -q x E
Therefore, the work done can be given as:
ΔW = -qE x Δ x = qV
Therefore E = - ΔV / Δx
This is the potential gradient.
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Electric Field and Potential due to a charged
sphere
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In a charged sphere the charge distributes itself evenly over the surface.
 Every part of the material of the conductor is at the same potential.
 Electric potential at a point is defined as
being numerically equal to the work done in bringing a unit positive
charge from infinity to that point, it has a constant value in every part
of the material of the conductor
 potential is the same at all points on the conducting surface, then
Δ V / Δx is zero. But E = - Δ V / Δ x.
 The electric field inside the conductor is zero. There is no electric field
inside the conductor.

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Equipotentials
 Regions in space where the electric potential of a
charge distribution has a constant value are called
equipotentials.
 The places where the potential is constant in three
dimensions are called equipotential surfaces, and
where they are constant in two dimensions they are
called equipotential lines.
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They are in some ways analogous to the contour lines on
topographic maps.
Similar also to gravitational potential.
In this case, the gravitational potential energy is constant
as a mass moves around the contour lines because the
mass remains at the same elevation above the earth's
surface.
The gravitational field strength acts in a direction
perpendicular to a contour line.
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Similarly, because the electric potential on an
equipotential line has the same value, no work can be
done by an electric force when a test charge moves on an
equipotential.
Therefore, the electric field cannot have a component
along an equipotential, and thus it must be everywhere
perpendicular to the equipotential surface or
equipotential line.
This fact makes it easy to plot equipotentials if the lines of
force or lines of electric flux of an electric field are
known.
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 For
example, there are a series of equipotential
lines between two parallel plate conductors that are
perpendicular to the electric field.
 There will be a series of concentric circles that map
out the equipotentials around an isolated positive
sphere.
 The lines of force and some equipotential lines for
an isolated positive sphere are shown in the next
figures.
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Analogies exist between electric and gravitational
fields.
(a) Inverse square law of force
Coulomb's law is similar in form to Newton's law of universal
gravitation.
 Both are inverse square laws with 1/(4πε) in the electric case
corresponding to the gravitational constant G.
 The main difference is that whilst electric forces can be attractive or
repulsive, gravitational forces are always attractive.
 Two types of electric charge are known but there is only one type of
gravitational mass.
 By comparison with electric forces, gravitational forces are extremely
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weak.

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 (b) Field strength
 The field strength at a point in a gravitational field is defined as the
force acting per unit mass placed at the point.
 Thus if a mass m in kilograms experiences a force F in newtons at a
certain point in the earth's field, the strength of the field at that point
will be F/m in newtons per kilogram.
 This is also the acceleration a the mass would have in metres per
second squared if it fell freely under gravity at this point (since F =
ma).
 The gravitational field strength and the acceleration due to gravity at a
point thus have the same value (i.e. F/m) and the same symbol, g, is
used for both. At the earth's surface g = 9.8 N kg-' = 9.8 m s-2
(vertically downwards).
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(c) Field lines and equipotentials
 These
can also be drawn to represent gravitational fields
but such fields are so weak, even near massive bodies, that
there is no method of plotting field lines similar to those
used for electric (and magnetic) fields.
 Field lines for the earth are directed towards its centre and
the field is spherically symmetrical.
 Over a small part of the earth's surface the field can be
considered uniform, the lines being vertical, parallel and
evenly spaced.
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(d) Potential and p.d.
 Electric potentials and pds are measured in joules
per coulomb (J C-1) or volts;
 gravitational potentials and pds are measured in
joules per kilogram (J kg-1).
 As a mass moves away from the earth the
potential energy of the earth-mass system
increases, transfer of energy from some other
source being necessary.
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 If
infinity is taken as the zero of gravitational
potential (i.e. a point well out in space where no
more energy is needed for the mass to move
further away from the earth)
 then the potential energy of the system will have
a negative value except when the mass is at
infinity.
 At every point in the earth's field the potential is
therefore negative (see expression below), a fact
which is characteristic of fields that exert
attractive forces.
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0bjectives covered
• 9.3.1
Define electric potential and electric potential energy.
• 9.3.2
State and apply the expression for electric potential due to a
point charge.
• 9.3.3
State and apply the formula relating electric field strength
to electric potential gradient.
• 9.3.4
Determine the potential due to one or more point charges.
• 9.3.5
Describe and sketch the pattern of equipotential surfaces
due to one and two point charges.
• 9.3.6
State the relation between equipotential surfaces and
electric field lines.
• 9.3.7
Solve problems involving electric potential energy and electric
potential.
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NEXT UNIT IS ATOMIC
PHYSICS CORE
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