chapter (3) electric potential - higher technological...
TRANSCRIPT
Chapter (3)Electric Potential
Defined
Electric Potential
Electric Potential Energy
Electric Potential Difference
Electric Potential Energy Difference
Equipotential Surfaces
Calculating the Potential from the Field
Potential Due to a Point Charge
Potential Due to a Group of Point Charges
Potential Due to an Electric Dipole
Electric Potential Energy of a System of Point Charges
Potential of a Charged Isolated Conductor
October 3, 2007
Potential Energy, Work and Conservative Force
Start
Then
So
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The work done by a conservative force
on a particle moving between any twopoints is independent of the pathtaken by the particle.
The work done by a conservative force
on a particle moving through anyclosed path is zero.
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gm
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The potential energy of the system
The work done by the electrostaticforce is path independent.
Work done by a electric force or ―field‖
Work done by an Applied force
Electric Potential Energy
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Example 1
A proton, located at point A in an electric field, has an electric potential energy of UA = 3.20 ×10-19 J. The proton experiences an average electric force of 0.80 × 10-9 N, directed to the right. The proton then moves to point B, which is a distance of 1.00 × 10-10 m to the right of point A. What is the electric potential energy of the proton at point B ?
October 3, 2007
Just as with potential energy, only differences in electric potential aremeaningful.
Relative reference: choose arbitrary zero reference level for ΔU or ΔV.
Absolute reference: start with all charge infinitely far away and set Ui = 0,
then we have and at any point in an electric field,where W is the work done by the electric field on a charged particle as that
particle moves in from infinity to point f.
SI Unit of electric potential: Volt (V)
1 volt = 1 joule per coulomb
1 J = 1 VC and 1 J = 1 N m
Electric field: 1 N/C = (1 N/C)(1 VC/J)(1 J/Nm) = 1 V/m
Electric energy: 1 eV = e(1 V)
= (1.60×10-19 C)(1 J/C) = 1.60×10-19 J
Electric Potential
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Notes
Electric field always points from higher electric potential to lower electric potential.
A positive charge accelerates from a region of higher electric potential energy (or higher potential) toward a region of lower electric potential energy (or lower potential).
A negative charge accelerates from a region of lower potential toward a region of higher potential.
Conceptual Example The Accelerations of Positive
and Negative Charges
Three points, A, B, and C, are located along a horizontal
line, as Figure 19.4 illustrates. A positive test charge is released from rest at A and accelerates toward B. Upon reaching B, the test charge continues to accelerate toward C. Assuming that only motion along the line is possible, what will a negative test charge do when it is released from rest at B?
Example 2 Work, Electric Potential Energy, and Electric Potential
The work done by the electric force as the test charge(q0=+2.0×10–6 C) moves from A to B is WAB=+5.0×10–5
J. (a) Find the difference, ΔU=UB–UA, in the electricpotential energies of the charge between these points.(b) Determine the potential difference, ΔV=VB–VA,between the points.
Example 3 Electric Field and Electric
Potential
Two identical point charges (+2.4×10–9 C) are fixed in
place, separated by 0.50 m. (see Figure 19.32). Find the electric field and the electric potential at the midpoint of the line between the charges qA and qB.
October 3, 2007
uphill for
q Electric field lines always point in the
direction of decreasing electricpotential.
A system consisting of a positivecharge and an electric field loseselectric potential energy when thecharge moves in the direction of thefield (downhill).
A system consisting of a negativecharge and an electric field gainselectric potential energy when thecharge moves in the direction of thefield (uphill).
Potential difference does not dependon the path connecting them
Potential Difference in a Uniform Electric Field
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October 3, 2007
Equipotential Surface The name equipotential surface is given to any
surface consisting of a continuous distributionof points having the same electric potential.
Equipotential surfaces are always perpendicularto electric field lines.
No work is done by the electric field on acharged particle while moving the particle alongan equipotential surface.
The equipotential surface is like the ―height‖lines on a topographic map.
Following such a line means that you remain atthe same height, neither going up nor goingdown—again, no work is done.
Analogy to Gravity
October 3, 2007
The right figure shows a family of equipotential surfaces associated with the electric field due to some distribution of charges. V1=100 V, V2=80 V, V3=60 V, V4=40 V. WI, WII, WIII and WIV
are the works done by the electric field on a charged particle q as the particle moves from one end to the other. Which statement of the following is not true?
A. WI = WII
B. WIII is not equal to zero
C. WII equals to zero
D. WIII = WIV
E. WIV is positive
positive or negative?
Problem 1
The drawing shows a cross-sectional view of two
spherical equipotential surfaces and two electric field
lines that are perpendicular to these surfaces. When an
electron moves from point A to point B (against the
electric field), the electric force does +3.2×10–19 J of
work. What are the electric potential differences (a) VB–
VA, (b) VC–VB, and (c) VC–VA?
October 3, 2007
The electric potential energy Start
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The electric potential
Calculating Potential from the field
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Potential difference depends only
on the source charge distribution(Consider points i and f without
the presence of the test charge;
The difference in potential energy
exists only if a test charge ismoved between the points.
October 3, 2007
Potential Due to a Point Charge Start with (set Vf=0 at and Vi=V at R)
We have
Then
So
A positively charged particle produces a positive
electric potential.
A negatively charged particle produces a negative electric potential
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October 3, 2007
Potential due to a group of point charges
Use superposition
For point charges
The sum is an algebraic sum, not a vector sum.
E may be zero where V does not equal to zero.
V may be zero where E does not equal to zero.
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October 3, 2007
4. Which of the following figures have V=0 and E=0 at red point?
Electric Field and Electric Potential
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Potential Due to an Electric Dipole
Sample Problem
(a) In Fig. a, 12 electrons (of charge −e) are equally spaced and
fixed around a circle of radius R. Relative to V=0 at infinity, what
are the electric potential and electric field at the center C of the
circle due to these electrons?
(b) If the electrons are moved along the circle until they are
nonuniformly spaced over a 120° arc (Fig. b), what then is the
potential at C? How does the electric field at C change (if at all)?
October 3, 2007
Electric Potential Energy of a System of Point Charges
Start with (set Ui=0 at and Uf=U at r)
We have
If the system consists of more than two charged
particles, calculate U for each pair of charges and sum the terms algebraically.
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The electric potential energy of a system of fixed point charges is equal to the work that must be done by an external agent to assemble the system, bringing each charge in from an infinite distance.
Sample Problem
The figure shows three point charges held in fixed positions by forces that are not shown. What is the electric potential energy U of this system of charges? Assume that d=12 cm and that
October 3, 2007
According to Gauss’ law, the charge resides on the conductor’s outer surface.
Furthermore, the electric field just outside the conductor is perpendicular to the surface and field inside is zero.
Since
Every point on the surface of a charged conductor in equilibrium is at the same electric potential.
Furthermore, the electric potential is constant everywhere inside the conductor and equal to its value to its value at the surface.
Potential Due to a Charged Isolated Conductor
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October 3, 2007
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Suppose that a positive test charge q0 moves through a displacement ds from on equipotential surface to the adjacent surface.
The work done by the electric field on the test charge is W = dU = -q0 dV.
The work done by the electric field may also be written as
Then, we have
So, the component of E in any direction is the negative
of the rate at which the electric potential changes with
distance in that direction.
If we know V(x, y, z),
Calculating the Field from the Potential
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October 3, 2007
Summary Electric Potential Energy: a point charge moves from i to
f in an electric field, the change in electric potential energy is
Electric Potential Difference between two points i and fin an electric field:
Equipotential surface: the points on it all have the same electric potential. No work is done while moving charge on it. The electric field is always directed perpendicularly to corresponding equipotential surfaces.
Finding V from E: Potential due to point charges: Potential due to a collection of point charges: Potential due to a continuous charge distribution: Potential of a charged conductor is constant everywhere
inside the conductor and equal to its value to its value at the surface.
Calculatiing E from V: Electric potential energy of system of point charges:
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