Download Electric Potential - PHYSICS I PRE-AP

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 Electric Potential
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Electric potential – electric potential energy per coulomb (j/c) at a location
in an
electric field; measured in volts and often called voltage.
Volt – in honor of Alessandro Volta, best know for having invented the electric
battery
1 volt = 1j/c
Two points are said to differ in electric potential if work is done to move a charge
from one point to another point in an electric field.
The effects of any charge distribution can be described either in terms of elelctric
field or in terms of electric potential.
Because electric potential is scalar it is often easier
Electric field is vector
The relationship between electric potential and electric fields is seen below.
Potential (symbol is V; SI unit is volt)
work done on a charge; or the electric potential is the potential energy per unit
charge. Only differences in potential can be measured.
V=W/q
In a uniform electric field (a parallel plate capacitor):
V=Ed
where E is the electric field strength and d is the separation between the plates in
meters
a positive plate has a higher potential than a negative plate
remember that charges move from positive to negative
a positive particle flows naturally from a high potential to a low potential and a
negative particle does the opposite.
Electric potential energy – energy a charge has due to its location in
an electric field.
Electric Potential Energy When a charge q moves from point B to point A in an
electric field, the change in electric potential energy is simply the negative of the
work done to move the same charge from point A to point B. Just as we defined
the electric field as the force per unit charge, we will define the electric potential
(or potential) as the potential energy per unit charge. If a point charge q has
-
electric potential energy of PEA at some point A, the electric potential at point A is
given by
VA = PEA / q
Since only differences in potential are measurable, the potential at point A would
simple be the difference in potential energy, or the work done, to move the charge
from some point B to point A.
VBA = VB - VA = WBA/q
The point at which there is the greatest potential energy is the point at which the
greatest amount of work can be done.
The greater the charge the greater the potential energy.
A negative sign in the result of PE indicates that the PE decreases.
The PE lost by a particle becomes KE
∆KE = ∆PE
½ mv2 – 0 = -qVba
Electric potential is a scalar term. When finding the electric potential due to a
collection of point charges, you need only add the potentials together with no
concern for direction. Include a sign for the potential corresponding to the sign of
the charge.
Clarifying the Difference Between Electric Energy and Potential
http://www.sciencejoywagon.com/physicszone/lesson/07elecst/potentil/epotenti.h
tm
Absolute Potential The electric potential at a distance r from a single point
charge can be derived from the expression for electric field due to a point charge.
Also called electric potential of a point charge. The expression for absolute
potential:
V=kq/r
Notes about Absolute Potential:
1. The potential of infinity is defined to be zero.
2. If a point charge is positive, the absolute potential of the charge is
positive. When moving a charge from infinity to this point, the potential
energy increases above a zero level.
3. If a point charge is negative, the absolute potential of the charge is
negative. When moving a charge from infinity to this point, the potential
energy decreased below a zero level.
4. To find the absolute potential of a configuration of multiple charges when
working problems, calculate the separate absolute potentials of each
charge. The absolute potential is thus negative if the charge is negative
and positive if the charge is positive. Add the absolute potentials with
these signs corresponding to the sign of the charge.
Electrostatic energy (U) for point charges can be found. It is simply the same
thing as "work" in the definition of voltage. Since the electric potential is defined
as the potential energy per unit charge, then the change in potential energy of
charge q moved between points a and b is simply equal to qVab. In other words,
U=qV
If dealing with point charges, U = qV becomes U = k (q1q2)/d. If one is trying to
find the total electrostatic energy due to a system of charges, one finds the sum of
the electrostatic energies between each charge. As in absolute potential, one
includes the sign of the charge.
Relationship Between Electric Potential and Electric Field One can describe
the effects of charge distribution using either electric field or electric potential.
Electric potential can be easier to use than electric fields because it is a scalar
quantity rather than a vector quantity.
1. In a uniform field (such as between two parallel plates), the units for
electric field (N/C) can be written as V/m. We find that E = V/d in a
uniform field.
2. In a non-uniform field (such as produced by a point charge), the electric
field in a given direction at any point in space is equal to the rate at which
the electric potential changes over distance in that direction.
Equipotential Lines Just as electric field lines represented the electric field
around a charge, equipotential lines represent the electric potential about a charge.
In three dimensions, they become equipotential surfaces.
Equipotential Surface An equipotential surface is one on which all points are at
the same potential. The potential difference between any two points on an
equipotential surface is zero; there is no work done to move a charge between
these two points.
An Animation Showing Equipotential Lines
http://www.sciencejoywagon.com/physicszone/lesson/07elecst/potentil/potlines.ht
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Characteristics of Equipotential Surfaces
1. No work is done to move a charge between two points on the same
equipotential surface.
2. Electric field lines are perpendicular to equipotential surfaces.
3. The surface of a conductor is an equipotential surface. (A conductor must
be entirely at the same potential in statics. There is no electric field within
a conductor in statics because otherwise an electron would experience a
force and would move.)
Electron Volt (eV) A unit used to deal with the energy of electrons. One electron
volt is defined as the energy acquired by a particle carrying a charge equal to that
of the electron as a result of moving through a potential difference of 1 V. It is not
an SI unit, just an easier unit to use than Joules sometimes.
1 eV = 1.6 x 10-19 J
Millikan’s oil drop experiment
Accurately measured the charge of an electron
Eq=mg
Where E is the electric field, q is the charge in Coulombs, and mg is the weight in
Newtons
AP Multiple Choice questions:
1. You may be asked to perform a simple calculation determining the electric
potential at some point P a distance d from a point charge (remember to
use V=kq/d).
2. Remember the definition of potential difference - it is the work done on a
charge. If they tell you how much work is done on a certain charge, you
can apply this definition to determine the potential difference.
3. They can give you two charges on the x-axis, noting several points either
outside or between them, and ask you at which point the electric potential
is the greatest, the least, or zero.
4. They may give you charges in a square or triangle and ask you what is the
potential of a charge held at point P. (Read notes above on electrostatic
energy, U).
AP Free Response questions:
1. They could give you an array of charges (in a square or a triangle) and ask
you to determine the electrostatic potential of the array at some point P.
They may also ask you to compare the work done to move a charge to this
point P compared to another array of charges.
2. A very common type of problem is to have a charge entering the region
between two parallel and charged plates of known voltage between them.
Again, remember the two important formulas, V=Ed and qV=W. The first
is used to calculate E when V and d are known. The second is used to
calculate speed when V is known.
3. In this same type of problem, they may ask you to draw the forces on the
charge using a free-body diagram. They may ask you to draw the path of
the charge between the two plates. They may apply mechanics concepts,
asking you to calculate speed, time, or vertical displacement of the charge
as it travels between the two plates. Remember, the vertical acceleration is
due to the electric field (you can ignore gravity because the charge isn't
between the plates long enough for it to have an effect). The horizontal
acceleration is zero so the time required to move through the region is
found using d=vt.
Sharing of Charge
In a conductor, charges move until all parts of a conductor are at the same
potential. If a large and a small sphere have the same total charge, the large sphere
will have a lower potential. If a large and a small sphere have the same potential,
the large sphere will have the greater charge.
Grounding
the potential of the earth is zero. Any object connected to the earth will have its
excess charge flow into the earth. It is considered to be grounded.
Electrostatic charges are only found on the outside of conductors.
Capacitors
Capacitor
a device (sometimes called a condenser) that stores charge in the electric field
between its plates. Each plate carries the same amount of charge, one plate being
negative and the other being positive. A potential difference exists between the
two plates.
Capacitance
symbol is C and SI unit is the Farad, F
q=CV
where q is the charge in Coulombs, C is the capacitance, and V is the potential
difference.
Capacitance for a parallel-plate capacitor Capacitance is a proportionality
constant. It is a constant for a given capacitor. It does not depend upon charge or
voltage. Its value only depends upon the structure and dimensions of the capacitor
itself. For a parallel-plate capacitor with plates of area A separated by a distance d
of air, the capacitance is given by: This relationship makes sense. Plates with a
larger area will have less repulsion between charges (they're further apart) for a
given amount of charge q. Thus, more charge can be held. A greater separation
means that the charge on each plate exerts less attractive force on the other plate.
Less charge is drawn from the battery, and the capacitance is less. Notice the use
of the permittivity of free space constant (We learned in our previous unit how
Coulomb's constant was related to the permittivity of free space.)
Dielectric An insulating sheet found in most capacitors between the plates. A
dielectric allows higher voltages to be applied without charge crossing the gap. A
dielectric allows the plates to be placed closer together without touching, allowing
an increased capacitance. A dielectric increases the capacitance by a factor K,
which is known as the dielectric constant. For a parallel-plate capacitor, C = K Co,
where Co is the capacitance without the capacitor.
It requires energy to place charges on the plates of a capacitor. When the
capacitor is discharged, this electrical energy is released. The energy stored in a
capacitor is equal to the work done to charge it.
Energy = ½ C V2 = 1/2 q V
Where C is the capacitance, q is the charge, and V is the voltage
When a DC voltage source is connected across an uncharged capacitor, the rate at
which the capacitor charges up decreases as time passes. At first, the capacitor is
easy to charge because there is little charge on the plates. But, as the charge
accumulates, more and more work is needed to move additional charges on the
plates because the plates already have charge of the same sign on them. As a
result, the capacitor charges exponentially, quickly at the beginning and more
slowly as the capacitor becomes fully charged. At any time, the charge on the
plates is given by:
Half-life
The time it takes the capacitor to reach half full is called the half-life and is
related to the time capacitive time constant in the following way:
half-life = RC ln 2
where R is resistance in ohms and C is capacitance in Farads
Storage of Electric Energy
A charged capacitor stores electric energy
Energy stored in the capacity will be equal to the work done to charge it.
Energy stored in a capacitor is :
U = ½ QV
Since Q=CV…..U=1/2 QV = ½ CV2 = ½ Q2/C
Energy density - Energy per unit volume
U = energy density = energy/volume = U/Ad= ½ ε0E2
Important things to remember about capacitors on the AP test:
1. The electric field between the two charged plates is uniform, the same
magnitude and direction at all points, neglecting edge effects.
2. You can use the direction of the electric field to predict the path a charged
particle will take between the two plates. For example, if it is an electron
and the top plate is positive, it will be deflected upward.
3. Important formulas to remember: V=Ed and qV=W. The first can be used
to calculate the electric field intensity between the two plates. The second
can be used to determine the increase in kinetic energy of the particle as it
passes between the two plates. This allows you to calculate speed.
Capacitors in Series and Parallel Combinations in Circuits
Equivalent Capacitance The capacitance of a single capacitor that can be
substituted for a combination of capacitors
1. Parallel combination of capacitors:
o To find the equivalent capacitance, add the individual
capacitances.
2. Series combination of capacitors:
o To find the reciprocal of the equivalent capacitance, add the
reciprocals of the individual capacitances.
Cathode Ray Tube
Composed of a cathode, the negative electrode, and an anode, positive electrode sealed in
a vacuum tube.
These terms were coined by Michael Faraday.
Thermionic emission, discovered by Thomas Edison
The cathode is heated causing electrons to travel to the positive anode. These electrons
were once called Cathode Rays. The electron beams are directed to various parts of a
screen to produce a picture. The inside of the tube is coated with fluorescent material
that will glow when excited. The electron beam sweeps across the screen in 525 lines.
High density televisions have twice the number of sweeps.
Oscilloscope – device for amplifying, measuring , and visually observing an electrical
signal.
AP Multiple Choice questions:
1. There are a surprising number of capacitor questions on the AP test.
2. They ask questions in which the separation between the plates and/or the
area of the plates is changed and how that affects charge and/or voltage.
3. They give you two capacitors in parallel (almost always, but sometimes in
series) and ask you what is the equivalent capacitance or how much charge
is stored in one of the capacitors. Remember, capacitors add in parallel
and q=CV.
4. You might be asked to calculate the energy stored in a capacitor.
AP Free Response questions:
1. Not very common except as two charged plates.
2. You could be given a capacitor of known capacitance and voltage and
asked to calculate the charge stored on it.
3. As part of the same problem, a dielectric may be inserted between the
plates of the capacitor. They will ask you what the potential difference is
(same) and what the electric field is (can be calculated using V=Ed).
4. They can ask you for calculations for a capacitor requiring that you know
C=kA/d.