Semester 2: Equations Flashcards
What is the equation for the electric field?
E = electric field
∇ = del operator
V = electrostatic potential
What is the equation for the difference in potential for two points in space?
V = potential between two points
E = electric field
Define Stokes’ theorem
The statements ∇ x E = 0 and ∫E . dl = 0 are equivalent.
Define Gauss’ law
The total electric flux out of a closed surface is equal to the total enclosed electric charge divided by a constant.
E = electric field
Q = charge
ε₀ = permittivity of free space
What is the equation for the electric field of a point charge?
E = electric field
q = charge
ε₀ = permittivity of free space
r = distance from point charge
What is the equation for the electric potential around a point charge?
V = electric potential
q = charge
ε₀ = permittivity of free space
r = distance from point charge
Define the divergence theorem
The flux of any vector field through a closed surface, S, can be related to the divergence of the vector field integrated over the volume enclosed by that surface.
What is the equation for the charge enclosed by a volume?
Q = charge
ρ = charge density
What is the differential form of Gauss’ law?
The divergence of the electric field at every point in space is given by the charge density at that location, divided by a constant (for any volume).
∇ = del operator
E = electric field
ρ = charge density
ε₀ = permittivity of free space
What is the equation for the principle of superposition for the electric fields of a set of point charges?
E = electric field
q = charge
ε₀ = permittivity of free space
r = distance from point charge
What is the equation for the principle of superposition for the electric potentials of a set of point charges?
V = electric potential
q = charge
ε₀ = permittivity of free space
r = distance from point charge
What is the equation for the electric field close to the surface of a charged conductor?
σ = charge per unit area
ε₀ = permittivity of free space
n = unit vector perpendicular to the surface
What is the equation for capacitance?
C = capacitance
Q = charge
V = difference between electrostatic potentials
What is the equation for the electric field between the plates of a parallel-plate capacitor?
E = electric field
σ = charge per unit area
ε₀ = permittivity of free space
What is the equation for the electric potential between the plates of a parallel-plate capacitor?
V = electric potential (difference)
E = electric field
σ = charge per unit area
d = separation distance
ε₀ = permittivity of free space
What is the equation for the capacitance of a parallel-plate capacitor?
C = capacitance
Q = charge
V = potential difference
σ = charge per unit area
A = area of plates
d = separation distance
ε₀ = permittivity of free space
What is the equation for the work done to charge a capacitor from 0 to Q?
U = work done
Q = charge
C = capacitance
V = potential difference
What is the equation for the energy stored in a capacitor in terms of the integrals for potential difference and charge?
U = energy stored
ε₀ = permittivity of free space
E = electric field
What is the equation for the energy density of a uniform electric field?
u_E = Energy density
ε₀ = permittivity of free space
E = electric field
Define Poisson’s equation
∇ = del operator
V = potential difference
∇² = Laplacian operator
ρ = charge density
ε₀ = permittivity of free space
Define Poisson’s equation in a vacuum (free space)
∇² = Laplacian operator
V = potential difference
What is Laplace’s equation in Cartesian coordinates?
What is the equation for the electric potential for a pair of point charges?
V = electric potential
q = charge
ε₀ = permittivity of free space
r = distance to charge
What are the equations for the electric field of a dipole in spherical polar coordinates (in r and θ directions)?
E = electric field
p = magnitude of the dipole moment
ε₀ = permittivity of free space
r = distance from the centre of the dipole