text
stringlengths
2
2.33k
source
stringclasses
826 values
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=∮SE→·n^dA=∮SE→·dA→,Φ=∮SE→·n^dA=∮SE→·dA→,where the notation used here is for a closed surfaceS.
https://openstax.org/books/university-physics-volume-2/pages/6-summary
Gauss’s law relates the electric flux through a closed surface to the net charge within that surface,Φ=∮SE→·n^dA=qencε0,Φ=∮SE→·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 whichE→·n^=EE→·n^=E, whereEis constant over the surface. The electric field is then determined with Gauss’s law.
https://openstax.org/books/university-physics-volume-2/pages/6-summary
For spherical symmetry, the Gaussian surface is also a sphere, and Gauss’s law simplifies to4πr2E=qencε04πr2E=qencε0.
https://openstax.org/books/university-physics-volume-2/pages/6-summary
For cylindrical symmetry, we use a cylindrical Gaussian surface, and find that Gauss’s law simplifies to2πrLE=qencε02πrLE=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 Gauss’s 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=σε0E=σε0.
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 ∑ i N ∑ j N q i q j r i j for i ≠j W 12 ⋯ N = k e 2 ∑ i N ∑ j N q i q j r i j for i ≠j
https://openstax.org/books/university-physics-volume-2/pages/7-key-equations
Δ V = Δ U q or Δ U = q Δ V Δ V = Δ U q or Δ U = q Δ V
https://openstax.org/books/university-physics-volume-2/pages/7-key-equations
V = U q = − ∫ R P E → ⋠d l → V = U q = − ∫ R P E → ⋠d l →
https://openstax.org/books/university-physics-volume-2/pages/7-key-equations
Δ V A B = V B − V A = − ∫ A B E → · d l → Δ V A B = V B − V A = − ∫ A B E → · d l →
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 ∑ 1 N q i r i V P = k e ∑ 1 N q i r i
https://openstax.org/books/university-physics-volume-2/pages/7-key-equations
p → = q d → p → = q d →
https://openstax.org/books/university-physics-volume-2/pages/7-key-equations
V P = k e p → · r ^ r 2 V P = k e p → · r ^ r 2
https://openstax.org/books/university-physics-volume-2/pages/7-key-equations
V P = k e ∫ d q r V P = k e ∫ d q r
https://openstax.org/books/university-physics-volume-2/pages/7-key-equations
E x = − ∂ V ∂ x , E y = − ∂ V ∂ y , E z = − ∂ V ∂ z E x = − ∂ V ∂ x , E y = − ∂ V ∂ y , E z = − ∂ V ∂ z
https://openstax.org/books/university-physics-volume-2/pages/7-key-equations
∇ → = i ^ ∂ ∂ x + j ^ ∂ ∂ y + k ^ ∂ ∂ z ∇ → = i ^ ∂ ∂ x + j ^ ∂ ∂ y + k ^ ∂ ∂ z
https://openstax.org/books/university-physics-volume-2/pages/7-key-equations
E → = − ∇ → V E → = − ∇ → V
https://openstax.org/books/university-physics-volume-2/pages/7-key-equations
∇ → = r ^ ∂ ∂ r + φ ^ 1 r ∂ ∂ φ + z ^ ∂ ∂ z ∇ → = r ^ ∂ ∂ r + φ ^ 1 r ∂ ∂ φ + z ^ ∂ ∂ z
https://openstax.org/books/university-physics-volume-2/pages/7-key-equations
∇ → = r ^ ∂ ∂ r + θ ^ 1 r ∂ ∂ θ + φ ^ 1 r sin θ ∂ ∂ φ ∇ → = r ^ ∂ ∂ r + θ ^ 1 r ∂ ∂ θ + φ ^ 1 r sin θ ∂ ∂ φ
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 asp→=qd→p→=qd→for 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,VB−VA,VB−VA,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 symbolΔVΔV:ΔV=ΔUqorΔU=qΔV.ΔV=ΔUqorΔU=qΔV.
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=(1.60×10−19C)(1V)1eV=(1.60×10−19C)(1V)=(1.60×10−19C)(1J/C)=1.60×10−19J.=(1.60×10−19C)(1J/C)=1.60×10−19J.
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=ke∑1NqiriVP=ke∑1Nqiri.
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 momentp→=qd→p→=qd→.
https://openstax.org/books/university-physics-volume-2/pages/7-summary
Continuous charge distributions may be calculated withVP=ke∫dqrVP=ke∫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 π ε 0 R 1 R 2 R 2 − R 1 C = 4 π ε 0 R 1 R 2 R 2 − R 1
https://openstax.org/books/university-physics-volume-2/pages/8-key-equations
C = 2 π ε 0 l ln ( R 2 / R 1 ) C = 2 π ε 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 → i = ( 1 κ − 1 ) E → 0 E → i = ( 1 κ − 1 ) E → 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 capacitor’s 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