Electrostatics

Electric charge

$$q = n\cdot e$$

q - charge
n - number of particles
e - electron charge

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$$F = \frac{k\cdot q1\cdot q2}{r^{2}}$$

F - force
k - proportionality coefficient
q1, q2 - charges
r - distance

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Coulomb constant

$$k = \frac{1}{4\cdot \pi\cdot \varepsilon_0}$$

k - proportionality coefficient
ε_0 - permittivity constant

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Relative dielectric constant (permittivity)

$$\varepsilon = \frac{F_{vak}}{F_{apl}}$$

ε - dielectric constant (permittivity)
F_vac - force in vacuum
F_env - force in environment

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$$E = \frac{F}{q}$$

E - electric field
F - force
q - charge

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Electric field of point charge in vacuum

$$E = \frac{k\cdot q_0}{r^{2}}$$

E - electric field
k - proportionality coefficient
q_0 - charge
r - distance

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Electric field of point charge in environment

$$E_{apl} = \frac{k\cdot q_0}{\varepsilon\cdot r^{2}}$$

E - electric field
k - proportionality coefficient
q - charge
ε - dielectric constant (permittivity)
r - distance

Find It is known that:

Calculate 'E_env'

Electric field outside charged sphere

$$E = \frac{k\cdot \sigma4\cdot \pi\cdot R^{2}}{r^{2}}$$

E - electric field
k - proportionality coefficient
σ - surface charge density
R - radius
r - distance

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Electric field outside charged sphere

$$E = \frac{k\cdot q}{r^{2}}$$

E - electric field
k - proportionality coefficient
q - charge
r - distance

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Electric field of infinite charged plane

$$E = k2\cdot \pi\cdot \sigma$$

E - electric field
k - proportionality coefficient
σ - surface charge density

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Electric field of infinite charged plane

$$E = \frac{\sigma}{2\cdot \varepsilon_0}$$

E - electric field
σ - surface charge density
ε_0 - permittivity constant

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Electric field of condenser (capacitor)

$$E = 4\cdot k\cdot \pi\cdot \sigma$$

E - electric field
k - proportionality coefficient
σ - surface charge density

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Work in an electric field

$$A = F\cdot \Delta_{d}$$

A - work
F - force
Δd - distance

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Potential energy of a system of two point charges

$$W = \frac{k\cdot q0\cdot q}{\varepsilon\cdot r}$$

W - potential energy
k - proportionality coefficient
q0, q - charges
ε - dielectric constant (permittivity)
r - distance

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Work in an electric field - potential energy difference

A - work
W1 - initial potential energy
W2 - final potential energy

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Potential of electrostatic field

$$\phi = \frac{W}{q}$$

φ - potential
W - potential energy
q - charge

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Voltage - potential difference

$$U = \phi1-\phi2$$

U - voltage
φ1 - initial potential
φ2 - final potential

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The work of the charge transfer

$$A = q\cdot U$$

A - work
q - charge
U - voltage

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Electrostatic potential around a point charge

$$\phi = \frac{k\cdot q0}{\varepsilon\cdot r}$$

φ - potential
k - proportionality coefficient
q_0 - charge
ε - dielectric constant (permittivity)
r - distance

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Electrostatic field strength

$$E = \frac{U}{\Delta_{d}}$$

E - electric field
U - voltage
Δd - distance

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Total electric field

E - total electric field
E0 - external electric field
E1 - internal electric field

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Electric moment

$$p = q\cdot l$$

p - electric moment
q - charge
l - distance

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Electric capacitance

$$C = \frac{q}{\phi}$$

C - electric capacitance
q - charge
φ - potential

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Electric capacitance of sphere

$$C = \frac{\varepsilon\cdot R}{k}$$

C - electric capacitance
ε - dielectric constant (permittivity)
R - radius
k - proportionality coefficient

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Electric capacitance of two conductors

$$C = \frac{q}{U}$$

C - electric capacitance
q - charge
U - voltage

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Electric capacitance of plane capacitor

$$C = \frac{\varepsilon\cdot \varepsilon0\cdot S}{d}$$

C - electric capacitance
ε - dielectric constant (permittivity)
ε0 - permittivity constant
S - area
d - the distance between the plates

Find It is known that:

Electric capacitance of spheric capacitor

$$C = \frac{4\cdot \pi\cdot \varepsilon\cdot \varepsilon0\cdot R1\cdot R2}{R2-R1}$$

C - electric capacitance
ε - dielectric constant (permittivity)
ε0 - permittivity constant
R1 - radius of the inner sphere
R2 - radius of outer sphere

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Potential energy of a charged plane capacitor

$$W = q\cdot E1\cdot d$$

W - potential energy
q - charge
E1 - electric field of one plate
d - the distance between the plates

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Potential energy of a charged plane capacitor

$$W = \frac{q\cdot E\cdot d}{2}$$

W - potential energy
q - charge
E - electric field
d - the distance between the plates

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Potential energy of a charged plane capacitor

$$W = \frac{q\cdot U}{2}$$

W - potential energy
q - charge
U - voltage

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Potential energy of a charged plane capacitor

$$W = \frac{C\cdot U^{2}}{2}$$

W - potential energy
C - electric capacitance
U - voltage

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Potential energy of a charged plane capacitor

$$W = \frac{q^{2}}{2\cdot C}$$

W - potential energy
q - charge
C - electric capacitance

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Potential energy of a charged plane capacitor

$$W = \frac{\varepsilon\cdot \varepsilon0\cdot E^{2}\cdot V}{2}$$

W - potential energy
ε - dielectric constant (permittivity)
ε0 - permittivity constant
E - electric field
V - bulk (volume)

Find It is known that:

Potential energy of a charged plane capacitor

$$W = \frac{\varepsilon\cdot \varepsilon0\cdot E^{2}\cdot S\cdot d}{2}$$

W - potential energy
ε - dielectric constant (permittivity)
ε0 - permittivity constant
E - electric field
S - area
d - the distance between the plates

Find It is known that:

Energy density of electric field

$$\omega_{p} = \frac{W}{V}$$

ω_p - energy density of electric field
W - potential energy
V - bulk (volume)

Find It is known that:

Calculate 'ω_p'

Energy density of electric field

$$\omega_{p} = \frac{\varepsilon0\cdot \varepsilon\cdot E^{2}}{2}$$

ω_p - energy density of electric field
ε0 - permittivity constant
ε - dielectric constant (permittivity)
E - electric field

Find It is known that:

Calculate 'ω_p'