PHYS 2002 Ch. 19
If the potential difference between the plates of the parallel plate capacitor is 5 Volts (ΔV = 5V)
"the voltage across the capacitor is 5 volts" distance across plates Δs is usually represented by d E = V/d for parallel plate capacitor
the work done on an object by a conservative force depends only on that objects ???
change in initial and final position work does not depend on the path taken
Work = change in ____ energy
change in potential energy
the electric field lines point in the direction of
decreasing potential
The potential at a distance r from a positive point charge is +V. What is the potential at a distance of r/3? V = kq/r
+3V
when the work done by non-conservative forces is equal to zero...
...the total mechanical energy is a constant of the motion Ef = Eo
Electric Field Equation
E = F/q
energy density
Rearrange: EPE = (1/2)(kεo)(E^2)(Ad) Ad = volume btwn plates EPE = 1/2KεoE^2(vol) EPE/vol = energy density = 1/2kεoE^2
In the previous question, the work done by the electrostatic force in moving the positive charge from Point B to Point C (middle to negative) (WBC) would be equal to which of the following?
The difference in the electrostatic potential energy between Points B (middle) and C (negative) (EPEB - EPEC).
electric field lines for a positive point charge
pass through the equipotential surfaces and are everywhere perpendicular to them perpendicular relationship is valid for all equipotential surfaces and electric field lines, not just for spherical surfaces around point charges
When the electric charge moves from point A to point B due to the electrostatic force...
...it loses electrostatic potential energy and gains kinetic energy
a conservative force allows definition of a _______ associated with the force
potential
Show quantitative relationship between electric field and equipotential surface in a parallel plate capacitor
the equipotential surfaces will be composed of an infinite set of parallel planes, where each plane is at a constant potential
parallel plate capacitor filled with dielectric capacitance
C = KεoA / d Farads (F)
electric dipole electric field lines
More complicated, but the equipotential surfaces must still be everywhere perpendicular to the electric field lines
_______ charges accelerate from regions of lower electric potential towards regions of higher electric potential (neg to pos)
Negative
Coulomb's law is similar to which other law?
Newton's universal law of gravitation both are inverse square laws both depend on a fundamental constant of nature both are directly proportional to the product of two charges or two masses both conservative forces
The electric field created by any charge or group of charges is everywhere perpendicular to
to the associated equipotential surfaces and points in the direction of decreasing potential
In general, a capacitor consists of...
two conductors of any shape placed near one another without touching
The difference in potential between two points in space depends on
the work done in moving the charge between those two points
Electrostatic Potential (V)
ΔEPE / q potential energy per unit charge (divided by a test charge) *work per unit charge* EPE = qo*V Units: J/C = volt V
The potential difference between the equipotential surface planes in a parallel plate capacitor
ΔV = VB-VA = -WAB/qo B is at negative plate (low V), A is at positive plate (high V) Work done to move a positive charge from point A to point B WAB = FΔs F = constant electrostatic force acting on the charge Δs = distance between the plates WAB = FΔs = qoEΔs
picofarad
the unit of measurement used to measure the strength of a capacitor 10^-12
microfarad
the unit of measurement used to measure the strength of a capacitor 10^-6 F
If a charge is moving along an equipotential surface...
the voltage doesn't change VA = VB WAB = 0
The drawing shows three arrangements of charged particles, all the same distance from the origin. Rank the arrangements, largest to smallest, according to the total electric potential V at the origin. A: -2q on -x, +6q on +x B: +4q on -x, -2q on +y C: +5q on -x, -3q on +x, +7q on +y, -5q on -y
A and C (a tie), B Correct answer iconCorrect. The total electric potential at the origin is the algebraic sum of the potentials due to all the charges. Since each potential is of the form V = kq/r (Equation 19.6) and r is same for each charge, the total electric potential is proportional to the sum of the charges. The sum of the charges in A (+4q) equals the sum in C (+4q), which is greater than the sum in B (+2q).
Which of the following statements is/are true? I. An equipotential surface is a surface of constant potential. II. The electrostatic force does no work on a charge that moves along an equipotential surface. III. The equipotential surfaces surrounding a point charge consist of an infinite number of concentric spherical shells. IV. Electric field lines are everywhere perpendicular to equipotential surfaces.
ALL OF THE ABOVE
The potential difference of the parallel plate capacitor The Potential Gradient
E = -ΔV/Vs units: volt/meter (V/m) N/C is equivalent to V/m
Relationship between electric field inside dielectric to field without dielectric
E = Eo/k = V/d without dielectric: E = q/εoA q = ((kεoA)/(d))/V
If the electrostatic force is the only force acting on the charge...
EPEB - EPEA = -ΔKE change in kinetic energy = work done on the object -ΔKE = -WAB
How do dipoles in a dielectric affect the electric field?
Each of the dipoles creates an internal electric field of their own that points in a direction opposite to that of the capacitors electric field reduces the net electric field between the plates, assuming the charge on the plates remains constant
Work is stored as electric potential energy in capacitor equations
Energy = 1/2qV q = CV V = q/C V = Ed C = KεoA/d EPE stored = 1/2CV^2 EPE stored = (1/2)(kεoA/d)(E^2d^2)
Which of the following would increase the capacitance of a parallel-plate capacitor? I. Insert a dielectric between the plates. II. Increase the surface area of each plate. III. Increase the separation distance between the plates.
I and II only
Three points A, B, and C are located along a horizontal line, as the figure shows. A positive charge is released from rest at point A and accelerates toward point B. Upon reaching B, it continues to accelerate toward C. If only motion along the line is allowed, what would a negative charge do if it were released from rest at point B?
It would accelerate toward A.
The Dielectric Constant
Often the space between the plates of a capacitor is filled with an insulating material (dielectric) The dielectric can increase the capacitance of the capacitor and allow it to store more charge alters electric field between the plates
_______ charges accelerate from regions of higher electric potential towards regions of lower electric potential (pos to neg)
Positive
A capacitor is charged with a battery to a voltage V and then disconnected from the battery. A dielectric is inserted between the plates. When the dielectric is inserted, what happens to the electrostatic potential energy stored in the capacitor?
The stored energy decreases.
How to charge a capacitor: battery
The battery acts like a pump that pulls electrons off one of the plates and pushes it to the other voltage of the battery plays the role of the pump pressure: greater voltage, more charge the battery can transfer The magnitude of the charge on each plate is directly proportional to the voltage
A proton is released from rest at point A in a constant electric field and accelerates to point B (see part a of the drawing). An electron is released from rest at point B and accelerates to point A (see part b of the drawing). How does the change in the proton's electric potential energy compare with the change in the electron's electric potential energy?
The change in the proton's electric potential energy is the same as the change in the electron's electric potential energy. Correct. The change in the proton's electric potential energy (EPEB - EPEA) in going from A to B is related to the change in the potential (VB - VA) by Equation 19.4 as EPEB - EPEA = (+e)( VB - VA), where +e is the charge on the proton. On the other hand, the change in the electron's electric potential energy (EPEA - EPEB) in going from B to A is related to the change in the potential (VA - VB) by EPEA - EPEB = (-e)( VA - VB), where -e is the charge on the electron. Comparing the right-hand sides of these two equations shows that the change in the proton's electric potential energy is the same as the change in the electron's electric potential energy.
A positive charge is placed between the plates of a parallel plate capacitor and released from rest at Point B (middle), as shown in the figure. In what direction does the charge move? (to positive A or negative C)
The charge moves toward Point C (negative).
How does the dielectric alter the electric field between the plates?
The charges in the molecules of the insulator are not free to move as they would be in a conductor They shift their position slightly in response to the capacitors electric field The electrons move towards the positive plate, and the positive charge in the molecule shifts toward the negative plate Molecular dipoles
Positive work
The direction of the force is in the same direction as displacement, object speeds up
Negative work
The direction of the force is opposite to displacement, object slows down
The electric potential V is constant everywhere within a certain region of space. Which statement below is true? The electric field varies from place to place within the region. The electric field is zero everywhere within the region. The electric field is also constant (but not zero) within the region. A charged particle placed within the region will experience an electric force.
The electric field is zero everywhere within the region. Correct. The electric field E is related to the electric potential difference ΔV by E = -ΔV/Δs (Equation 19.7), where Δs is the displacement of one point in the region relative to another point. If the potential is the same everywhere, then ΔV = 0 V, so E is zero everywhere.
The electric potential is constant throughout a certain region of space. What can you say about the electric field in this region?
The electric field is zero.
Definition: The Electric Potential V
The electric potential V at a given point is the electric potential energy EPE of a small test charge qo located at that point divided by the charge itself ΔEPE = Work
A proton and electron are simultaneously released from rest at the midpoint between the plates of a charged parallel-plate capacitor. Which particle strikes one of the plates first?
The electron.
A charge of +2Q and -2Q are located at two of the vertices of an equilateral triangle. Which of the following is true?
The potential at the triangle's empty vertex is zero.
Potential around a point charge V = kq/r
The potential has the same value in every direction at a distance r from the charge q
electrostatic potential difference or potential difference ΔV "voltage" because measured in volts
The potential is a measure of how much electrostatic potential energy a charge can get when placed at a particular location within an electric field ΔV = VB-VA = (EPEB/qo) - (EPEA/qo) = -WAB/qo The work depends on the differenced in potential and potential energy
Electrostatic Potential Energy EPE
The work done is equivalent to the electrostatic potential energy EPE. W = F*d F = q*E W = qE(yf-yo) W(AB) = ΔEPE Work to move something across distance from point A to B Joules
how much electrostatic potential energy would a fourth charge q4 have if placed at point P? - depends on sign of potential at point P and on the sign of q4
V = EPE/qo Find EPE, multiply by qo EPEq4 = q4Vp = q4(-k) J
The electric potential of a point charge at a distance r
V = kq/r when q is positive, v is positive when q is negative, v is negative a single point charge raises or lowers the potential at a given location depending on whether the charge is positive or negative if two or more charges are present, the total potential at a point in space near the charges is the scalar sum of the potentials from each of the charges
What is the potential at point P? Three charges on a rectangle and one empty point
Vp = V1 at p + V2 at p + V3 at p = kq1/r1 + kq2/r2 + kq3/r3
Work equations for capacitors storing energy
W=(q)(avg. V) avg. V = 1/2 V W = 1/2qV Energy = 1/2qV
equipotential surface
a surface of constant potential equipotential surfaces around a point charge = infinite number of concentric spherical shells
the surface of a conductor IS
an equipotential surface
work is only done when a charge moves _______ equipotential surfaces (from point A to point D) therefore, moves between different potentials
between equipotential surfaces
the capacitance of a parallel plate capacitor
electric field inside the dielectric between the plates of the parallel plate capacitor: E = V/d V = magnitude of potential difference between plates d = plate separation
Electric field is perpendicular to the associated equipotential surfaces BECAUSE
if there was a parallel component to the electric field, it would apply a force to a charge on the surface and do work on the charge if work is done, the potential must change (not possible on equipotential surface)
the potential decreases as the distance from the charge
increases
The electrostatic force that moves a test charge to or away from a point charge is
is not constant force is dependent on 1/r^2 as it moves away, the force continuously decreases
The dielectric constant
k (kappa) describes the reduction of the electric field defined as the ratio of the electric field without dielectric to the field with the dielectric ratio of two electric fields: unitless (greater than or equal to 1) value is material-dependent
electron volt
magnitude of the amount by which the potential energy of an electron changes when the electron moves through a potential difference of one volt
How is electrostatic potential energy analogous to gravitational potential energy? W = Δmgh = ΔGPE W = ΔqEy = ΔEPE
mgΔh = qEΔy mass magnitude = charge magnitude gravitational force = electrostatic force change in height = change in position
the net electric force does ________ on a charge as it moves on an equipotential surface
no work
capacitance of the capacitor
q = CV larger capacitance, greater amount of charge the capacitor can hold for a given voltage unit: C/V = farad (F)
calculating the work done in a point charge electrostatic force moving a test charge from point A to point B
represents the potential difference near the point charge
The main function of a capacitor is to...
store charge each plate holds the same magnitude of charge, one positive and one negative
The potential gradient gives only the component of
the electric field along the displacement Δs it can be applied to many situations where the potential changes from place to place
the net work done by a conservative force moving an object around in a closed path is ???
zero