Electrostatics equations Flashcards
What links force, charges in the field and radius?
F = k QQ/r^2 - Coulomb’s law
What 4 key properties does the electric force between charges have?
Like charges repel. Force acts along line between charges. Magnitude of force is inversely prop. to square of distance between charges. Force is proportional to product of charges magnitude
What links amps, coulombs and seconds?
1 Amp = 1 C/s
What shape is force distributed from a point charge?
Radially/Sphere
Why do we add epsilon r into Coulombs law?
Because the material affects force so the relative permittivity of the surrounding material is included.
What is Coulomb’s Law for two isolated point charges?
F = Q Q / 4πr^2 ε0εr
-Force here is a vector
What is ε0?
Permitivitty of free space(vacuum) (8.854x10^-12 C^2/NM^2)
What is εr?
Relative permittivity of the surrounding material (dimensionless) (=1 for free space)
What is the principle of superposition for charges?
Where multiple charges are present, the force experience by any charge is the vector sum of the forces on it from other charges.
What links Electric field, force and a test charge?
E = F/Qt
-E and F are vectors
For isolated charges what links Electric field strength, charge and radius?
E(vector) = Q/4πr^2 ε0
What do radial field lines show?
The direction of force for a positive test charge in that field.
What is an electric dipole?
Electric dipoles are pairs of equal but opposite point charges separated by some small fixed distance.
What equation for a dipole, links Torque, Electric field, charge and distance?
𝜏+ = 𝜏− = 𝐸𝑄(𝑑/2)sin 𝜃, therefore total torque on dipole is 𝜏 = 𝐸𝑄𝑑sin 𝜃
What links work, force and displacement?
Work = Force x displacement
What is an equation for Potential Energy with charges.
Work = Potential Energy = − ∫ 𝐸⃗ 𝑄𝑡 .𝑑𝑟⃗
Limits Ra and ∞
What links potential, charge and distance?
Potential =𝑄1 / 4𝜋𝑟 𝜀0
-Divide potential energy by Qt.
What is an equation for potential difference using two points a charge has moved between (rA and rB)?
Potential difference = − ∫ 𝐸⃗ .𝑑r
Limits rB and rA
What links Electric flux density, D(vector) and electric field strength?
D(vector) = 𝜀0𝜀r E(vector)
What links electric flux, electric flux density and area?
𝜓 = 𝐷⃗𝐴 cos θ
What is Gauss’ Law in words?
“the total electric
flux out of a surface is equal to the net charge enclosed by that surface”
What is Gauss’ Law, using S(closed surface), D(electric flux density), ψ(flux out of the surface), Q(charge enclosed)
ψ = ∯𝐷⃗𝑑𝑆⃗ = ∑𝑄𝑒𝑛𝑐
What is Gauss’ Law reduced for a Gaussian surface?
ψ = 𝐷𝑛𝑆 = ∑𝑄enc
Explain how to find electric field strength from Gauss’ Law for spherical Gaussian surface.
- ψ = 4𝜋𝑎^2𝐷 = 𝑄
- 𝐷 = 𝑄4𝜋𝑎^2
- 𝐸⃗ =𝐷⃗/𝜀0𝜀𝑟 = 𝑄/4𝜋𝜀0𝑎^2
What is capacitance?
A measure of a systems ability to store energy in an electric field.
What links capacitance, charge and voltage?
C = Q/V units Farads
What does capacitance depend on?
The physical properties of the system (its dimension and materials)
What links energy stored by a capacitor, Q, C and V
Energy stored = 1/2 Q^2/C = 1/2 QV = 1/2 CV^2
What links capacitance, area of plates, distance between them?
𝐶 = 𝐴𝜀0 / 𝑑
What is a dielectric material?
An insulator. In an electric field molecules within the material align their dipoles to produced a polarised material.
What links the electric field strength and electric flux density with dielectric materials?
E = D/𝜀0𝜀r
What is the charge enclosed within a conducting sphere?
It is zero. Therefore flux density and electric field are also zero.
What is the capacitance per metre for a Gaussian cylinder?
𝐶 = 2𝜋𝜀0𝜀𝑟 / ln(𝑏/𝑎)
