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spherical symmetry : system only varies with the distance from the origin, not in direction | https://openstax.org/books/university-physics-volume-2/pages/6-key-terms |
The electric flux through a surface is proportional to the number of field lines crossing that surface. Note that this means the magnitude is proportional to the portion of the field perpendicular to the area. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
The electric flux is obtained by evaluating the surface integralΦ=â®SEâ·n^dA=â®SEâ·dAâ,Φ=â®SEâ·n^dA=â®SEâ·dAâ,where the notation used here is for a closed surfaceS. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
Gaussâs law relates the electric flux through a closed surface to the net charge within that surface,Φ=â®SEâ·n^dA=qencε0,Φ=â®SEâ·n^dA=qencε0,whereqencqencis the total charge inside the Gaussian surfaceS. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
All surfaces that include the same amount of charge have the same number of field lines crossing it, regardless of the shape or size of the surface, as long as the surfaces enclose the same amount of charge. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
For a charge distribution with certain spatial symmetries (spherical, cylindrical, and planar), we can find a Gaussian surface over whichEâ·n^=EEâ·n^=E, whereEis constant over the surface. The electric field is then determined with Gaussâs law. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
For spherical symmetry, the Gaussian surface is also a sphere, and Gaussâs law simplifies to4Ïr2E=qencε04Ïr2E=qencε0. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
For cylindrical symmetry, we use a cylindrical Gaussian surface, and find that Gaussâs law simplifies to2ÏrLE=qencε02ÏrLE=qencε0. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
For planar symmetry, a convenient Gaussian surface is a box penetrating the plane, with two faces parallel to the plane and the remainder perpendicular, resulting in Gaussâs law being2AE=qencε02AE=qencε0. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
The electric field inside a conductor vanishes. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
Any excess charge placed on a conductor resides entirely on the surface of the conductor. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
The electric field is perpendicular to the surface of a conductor everywhere on that surface. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
The magnitude of the electric field just above the surface of a conductor is given byE=Ïε0E=Ïε0. | https://openstax.org/books/university-physics-volume-2/pages/6-summary |
U ( r ) = k e q Q r U ( r ) = k e q Q r | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
W 12 ⯠N = k e 2 â i N â j N q i q j r i j for i â j W 12 ⯠N = k e 2 â i N â j N q i q j r i j for i â j | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
Î V = Î U q or Î U = q Î V Î V = Î U q or Î U = q Î V | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
V = U q = â â« R P E â â d l â V = U q = â â« R P E â â d l â | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
Î V A B = V B â V A = â â« A B E â · d l â Î V A B = V B â V A = â â« A B E â · d l â | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
V = k e q r V = k e q r | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
V P = k e â 1 N q i r i V P = k e â 1 N q i r i | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
p â = q d â p â = q d â | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
V P = k e p â · r ^ r 2 V P = k e p â · r ^ r 2 | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
V P = k e â« d q r V P = k e â« d q r | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
E x = â â V â x , E y = â â V â y , E z = â â V â z E x = â â V â x , E y = â â V â y , E z = â â V â z | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
â â = i ^ â â x + j ^ â â y + k ^ â â z â â = i ^ â â x + j ^ â â y + k ^ â â z | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
E â = â â â V E â = â â â V | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
â â = r ^ â â r + Ï ^ 1 r â â Ï + z ^ â â z â â = r ^ â â r + Ï ^ 1 r â â Ï + z ^ â â z | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
â â = r ^ â â r + θ ^ 1 r â â θ + Ï ^ 1 r sin θ â â Ï â â = r ^ â â r + θ ^ 1 r â â θ + Ï ^ 1 r sin θ â â Ï | https://openstax.org/books/university-physics-volume-2/pages/7-key-equations |
electric dipole : system of two equal but opposite charges a fixed distance apart | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
electric dipole moment : quantity defined aspâ=qdâpâ=qdâfor all dipoles, where the vector points from the negative to positive charge | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
electric potential : potential energy per unit charge | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
electric potential difference : the change in potential energy of a chargeqmoved between two points, divided by the charge. | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
electric potential energy : potential energy stored in a system of charged objects due to the charges | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
electron-volt : energy given to a fundamental charge accelerated through a potential difference of one volt | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
electrostatic precipitators : filters that apply charges to particles in the air, then attract those charges to a filter, removing them from the airstream | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
equipotential line : two-dimensional representation of an equipotential surface | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
equipotential surface : surface (usually in three dimensions) on which all points are at the same potential | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
grounding : process of attaching a conductor to the earth to ensure that there is no potential difference between it and Earth | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
ink jet printer : small ink droplets sprayed with an electric charge are controlled by electrostatic plates to create images on paper | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
photoconductor : substance that is an insulator until it is exposed to light, when it becomes a conductor | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
Van de Graaff generator : machine that produces a large amount of excess charge, used for experiments with high voltage | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
voltage : change in potential energy of a charge moved from one point to another, divided by the charge; units of potential difference are joules per coulomb, known as volt | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
xerography : dry copying process based on electrostatics | https://openstax.org/books/university-physics-volume-2/pages/7-key-terms |
The work done to move a charge from pointAtoBin an electric field is path independent, and the work around a closed path is zero. Therefore, the electric field and electric force are conservative. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
We can define an electric potential energy, which between point charges isU(r)=keqQrU(r)=keqQr, with the zero reference taken to be at infinity. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
The superposition principle holds for electric potential energy; the potential energy of a system of multiple charges is the sum of the potential energies of the individual pairs. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
Electric potential is potential energy per unit charge. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
The potential difference between pointsAandB,VBâVA,VBâVA,that is, the change in potential of a chargeqmoved fromAtoB, is equal to the change in potential energy divided by the charge. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
Potential difference is commonly called voltage, represented by the symbolÎVÎV:ÎV=ÎUqorÎU=qÎV.ÎV=ÎUqorÎU=qÎV. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
An electron-volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form,1eV=(1.60Ã10â19C)(1V)1eV=(1.60Ã10â19C)(1V)=(1.60Ã10â19C)(1J/C)=1.60Ã10â19J.=(1.60Ã10â19C)(1J/C)=1.60Ã10â19J. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
Electric potential is a scalar whereas electric field is a vector. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
Addition of voltages as numbers gives the voltage due to a combination of point charges, allowing us to use the principle of superposition:VP=keâ1NqiriVP=keâ1Nqiri. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
An electric dipole consists of two equal and opposite charges a fixed distance apart, with a dipole momentpâ=qdâpâ=qdâ. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
Continuous charge distributions may be calculated withVP=keâ«dqrVP=keâ«dqr. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
Just as we may integrate over the electric field to calculate the potential, we may take the derivative of the potential to calculate the electric field. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
This may be done for individual components of the electric field, or we may calculate the entire electric field vector with the gradient operator. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
An equipotential surface is the collection of points in space that are all at the same potential. Equipotential lines are the two-dimensional representation of equipotential surfaces. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
Equipotential surfaces are always perpendicular to electric field lines. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
Conductors in static equilibrium are equipotential surfaces. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
Topographic maps may be thought of as showing gravitational equipotential lines. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
Electrostatics is the study of electric fields in static equilibrium. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
In addition to research using equipment such as a Van de Graaff generator, many practical applications of electrostatics exist, including photocopiers, laser printers, ink jet printers, and electrostatic air filters. | https://openstax.org/books/university-physics-volume-2/pages/7-summary |
C = Q V C = Q V | https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
C = ε 0 A d C = ε 0 A d | https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
C = 4 Ï Îµ 0 R 1 R 2 R 2 â R 1 C = 4 Ï Îµ 0 R 1 R 2 R 2 â R 1 | https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
C = 2 Ï Îµ 0 l ln ( R 2 / R 1 ) C = 2 Ï Îµ 0 l ln ( R 2 / R 1 ) | https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
1 C S = 1 C 1 + 1 C 2 + 1 C 3 + ⯠1 C S = 1 C 1 + 1 C 2 + 1 C 3 + ⯠| https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
C P = C 1 + C 2 + C 3 + ⯠C P = C 1 + C 2 + C 3 + ⯠| https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
u E = 1 2 ε 0 E 2 u E = 1 2 ε 0 E 2 | https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
U C = 1 2 V 2 C = 1 2 Q 2 C = 1 2 Q V U C = 1 2 V 2 C = 1 2 Q 2 C = 1 2 Q V | https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
C = κ C 0 C = κ C 0 | https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
U = 1 κ U 0 U = 1 κ U 0 | https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
κ = E 0 E κ = E 0 E | https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
E â i = ( 1 κ â 1 ) E â 0 E â i = ( 1 κ â 1 ) E â 0 | https://openstax.org/books/university-physics-volume-2/pages/8-key-equations |
capacitance : amount of charge stored per unit volt | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
capacitor : device that stores electrical charge and electrical energy | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
dielectric : insulating material used to fill the space between two plates | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
dielectric breakdown : phenomenon that occurs when an insulator becomes a conductor in a strong electrical field | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
dielectric constant : factor by which capacitance increases when a dielectric is inserted between the plates of a capacitor | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
dielectric strength : critical electrical field strength above which molecules in insulator begin to break down and the insulator starts to conduct | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
energy density : energy stored in a capacitor divided by the volume between the plates | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
induced electric-dipole moment : dipole moment that a nonpolar molecule may acquire when it is placed in an electrical field | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
induced electrical field : electrical field in the dielectric due to the presence of induced charges | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
induced surface charges : charges that occur on a dielectric surface due to its polarization | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
parallel combination : components in a circuit arranged with one side of each component connected to one side of the circuit and the other sides of the components connected to the other side of the circuit | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
parallel-plate capacitor : system of two identical parallel conducting plates separated by a distance | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
series combination : components in a circuit arranged in a row one after the other in a circuit | https://openstax.org/books/university-physics-volume-2/pages/8-key-terms |
A capacitor is a device that stores an electrical charge and electrical energy. The amount of charge a vacuum capacitor can store depends on two major factors: the voltage applied and the capacitorâs physical characteristics, such as its size and geometry. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
The capacitance of a capacitor is a parameter that tells us how much charge can be stored in the capacitor per unit potential difference between its plates. Capacitance of a system of conductors depends only on the geometry of their arrangement and physical properties of the insulating material that fills the space bet... | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
When several capacitors are connected in a series combination, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
When several capacitors are connected in a parallel combination, the equivalent capacitance is the sum of the individual capacitances. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
When a network of capacitors contains a combination of series and parallel connections, we identify the series and parallel networks, and compute their equivalent capacitances step by step until the entire network becomes reduced to one equivalent capacitance. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
Capacitors are used to supply energy to a variety of devices, including defibrillators, microelectronics such as calculators, and flash lamps. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
The energy stored in a capacitor is the work required to charge the capacitor, beginning with no charge on its plates. The energy is stored in the electrical field in the space between the capacitor plates. It depends on the amount of electrical charge on the plates and on the potential difference between the plates. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
The energy stored in a capacitor network is the sum of the energies stored on individual capacitors in the network. It can be computed as the energy stored in the equivalent capacitor of the network. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
The capacitance of an empty capacitor is increased by a factor ofκκwhen the space between its plates is completely filled by a dielectric with dielectric constantκκ. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
Each dielectric material has its specific dielectric constant. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
The energy stored in an empty isolated capacitor is decreased by a factor ofκκwhen the space between its plates is completely filled with a dielectric with dielectric constantκκwhile disconnecting the battery and keeping the charge on the capacitor constant. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
When a dielectric is inserted between the plates of a capacitor, equal and opposite surface charge is induced on the two faces of the dielectric. The induced surface charge produces an induced electrical field that opposes the field of the free charge on the capacitor plates. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
The dielectric constant of a material is the ratio of the electrical field in vacuum to the net electrical field in the material. A capacitor filled with dielectric has a larger capacitance than an empty capacitor. | https://openstax.org/books/university-physics-volume-2/pages/8-summary |
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