Semester 2: Questions Flashcards
Give 2 examples of scalar quantities in electrostatics
- Electrostatic potential, V
- Potential energy, U = qV
Give 2 examples of vector quantities in electrostatics
- Electric field, E = - ∇ V
- Electric force, F = qE
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
Electric field lines are always _______ to the electrostatic potential contours
Perpendicular
Define a conservative field
A vector field whose line integral only depends on the end points of the line, not the path taken to get there (the integral around all closed paths is zero).
Show that an electric field can be conservative using vector calculus
∇ = del operator
E = electric field
_ x _ = curl
∇ x E = -∇ x ∇ V = 0
Define Stokes’ theorem (electromagnetism)
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.
What is the equation for Gauss’ law?
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 definition of and the equation for 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
Define the principle of superposition (for electric fields)
For a system of charged objects, the net electric field is equal to the vector sum of the fields of the individual charges.
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
Define the principle of superposition (for potentials)
For a system of charges, the total electrostatic potential is equal to the sum of the potential due to the individual charges.
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 a conductor?
Systems where charges are free to move. If an electric field is applied outside a conductor, the charges will move and redistribute inside the conductor until the force on them due to the electric field is zero.
What is the electric field inside a conductor in electrostatic equilibrium?
Zero
All points within a conductor are at the same ________ ________, also known as an ________________.
Electrostatic potential
Equipotential
What is the electric flux of a Gaussian surface enclosed within a conductor in electrostatic equilibrium?
Zero
Very close to the surface of a conductor, the electric field lines must be _________ to the surface of the conductor.
Perpendicular