IA: 1P3: Physical Principles of Electronics Flashcards
What is the equation for the scalar/dot product between 2 vectors, E and H?
E * H = EH cosθ
Where θ is the outgoing angle between vectors E and H
What does the scalar/dot product do?
use E * H as an example
It finds out how much of the vector E is in the same direction as the vector H
What does orthogonal mean?
Perpendicular
What does the cross/vector product do?
It finds a vector which is normal to the plane containing the first 2 vectors
What is the equation for the cross/vector product?
E x H = EH sinθ an
Where θ is the outgoing angle between the vectors E and H
Where an is the unit vector in the direction of the resulting vector
Explain why ExH ≠ HxE
The 2 resulting vectors will be in the opposite directions
What is the plane of incidence during a vector product?
The plane containing both of the original 2 vectors
What is the right hand rule for the cross product?
E = index finger
H = middle finger
ExH = thumb
What are cartesian coordinates?
Cartesian coordinates (x,y,z) form a right-handed orthogonal set
What are circular cylindrical coordinates?
Circular cylindrical coordinates (r, φ, z).
* r is a vector denoting a distance and direction away from the central origin
* φ (phi) is known as the azimuthal and is the angle between the positive x axis and the position in the x-y plane
What are spherical coordinates?
Spherical coordinates (r, θ, φ)
* r is a vector denoting a distance and direction away from the central origin
* θ (theta) is known as the zenithal and is the angle between the positive z axis and the coordinate
* φ (phi) is known as the azimuthal and is the angle between the positive x axis and the position in the x-y plane
When may circular cylindrical coordinates be useful?
Wires
When may spherical coordinates be useful?
- balls
- points
- spheres
What are the 5 steps to solving most electromagnetic problems?
- Identify what is being asked for
- Evaluate the geometry (line, sphere, tube)
- Choose the relevent relationship (Coulomb, Gauss, Virtual Work)
- Choose the material properties (Vacuum, dielectric, metals)
- Solve the maths!
What happens if there is an assymetry in electrons throughout a structure?
It is polarised
What is the assumption with electrostatics?
The charges are stationary
How are static charges assumed to be distributed in an insulating material?
Distributed throughout the volume of the material
How are static charges assumed to be distributed in a conducting material?
Uniformly distributed on the surface of the volume
What force would a charged point experience hanging inside a charged sphere?
no force, there is no electric field inside the sphere
What is the equation for coulombs law?
What is the value of the dielectric permittivity of free space?
8.854 x10⁻¹² Fm⁻¹
What is coulombs constant?
1/4πε₀
What is an electric field?
An electric field represents the lines of force surrounding charges in an electrostatic system, it is measured in volts per metre
How is the magnitude of an electrostatic force related to the distance from from a point charge?
F ∝ 1/r²
How is the strength of an electric field related to the distance from a point charge?
E ∝ 1/r²
What is the equation for coulombs law in term of vectors?
Where r hat is a unit vector
What is the equation for coulombs law in terms of electric field?
F = qE
What is the equation for an electric field in terms of vectors?
Explain electric field lines
Electric field lines always begin and end at a charged particle or point on a surface (even if they are at infinity). The strength of an electric field is only zero at infinity
When several charges are present how can you determine the electric field?
Through the superposition of each of the individual electric fields. The electric field is given by the vector summation of the fields arising from each of the individual charges.
What is the equation for the superposition of electric fields?
What happens to the charges in a material if they are subjected to an electric field?
- If it is a conductor, then the charges are free to move and a current will flow
- If it is a dielectric, the charges are bound inside the molecules and cannot move freely, however they can move within the molecule creating a charge imbalance (polarisation)
What happens to the electric field if you place a dielectric within a parallel plate capacitor?
The electric field between the 2 plates polarises the molecules within the dielectric, slightly separating the positive and negative charges. Throughout most of the dielectric the charges cancel, however at the surfaces a net positive and negative charge appears setting up a weak internal E field in the opposite direction to that applied by the capacitor. This results in a weaker field in the dielectric.
What is the equation for the relative electric fields within a capacitor and dielectric?
E₁ = εᵣE₂
Where εᵣ is the relative permittivity/dielectric constant of the material
What is dielectric breakdown?
The equation “E₁ = εᵣE₂” is only always true for perfect dielectrics, in reality materials are not perfect and so when the electric field is very large it will pull the electrons out of the molecules and cause the material to start conducting. This is usually highly catastrophic
What is the equation for the permitivity of a material?
ε = ε₀εᵣ
ε₀ = permittivity of free space
εᵣ = relative permittivity/dielectric constant of the material
When does dielectric breakdown occur?
When the dielectric strength, Eₘₐₓ, of the material is exceeded
What is the dielectric strength, Eₘₐₓ, of a material?
The maximum eelctric field a material can tolerate before breakdown occurs
What is constant between the 2 plates of a capacitor with a dielectric between the 2 plates?
Electric flux density, D
NOT Electric field, E
What is electric field displacement?
Electric flux density, D
What is Electric flux density, D?
A vector field that represents the electric flux per unit area passing through a region
What is the equation for electric flux density?
D = εE = ε₀εᵣE
Prove electric flux density is constant no matter the medium in which it is being analysed
What is flux conservation?
Electric flux density, D, has the propery that its normal component takes the same value on passing from one dielectric to another
This makes it very useful for dielectric problems as it avouds having to calculate the polarisation of charges and relative electric fields
What is the equation for the electric flux passing through a surface if the field is always perpendicular to the surface?
flux =|D|A
Where D is the electric flux density and A is the area of the surface
What is Gauss’s law?
The flux passing through a closed surface is equal to the charge that has been enclosed by the surface that was perpendicular to the electric flux density
Derive Gauss’s law using the electric field surrounding a point charge Q
What is a Gaussian surface?
A surface on which the electric flux density, D, is always perpendicular to
When is it useful to use Gauss’s law to calculate electric field strengths?
When there is a high degree of symmetry (and so a Gaussian surface can be formed)
What would the Gaussian surface for a point charge be?
A sphere
What would the Gaussian surface for an infinitely long wire be?
A cylinder
In which direction does D act from an infinitely long wire?
Radially - all horizontal components cancel out
Derive the equation for the electric field surrounding a wire with a charge density of ρ₁ per unit length
Why is there no electric field inside a hollow, charged conducting object
When considering a conductor, we assume the charges are distributed across the surface of the object. Therefore a Gaussian surface S inside the conductor must have zero flux through it, since it encloses zero charge (Gauss’s law). Hence, the electric field must be zero everywhere inside the hollow conducting shell as there is zero flux for a finite surface area.
Derive the equation for the electric field either side of a charged thin uniform metal plane with static charge evenly distributed with a density of α cm⁻²
E = α/2ε₀
What is electrostatic potential?
The work done when a unit positive charge is moved from one point to another in the presence of an electric field
What is the equation for the work done moving a unit charge a distance dl?
What is the equation for the total work done to move a unit charge from one point in an electric field to another point?
This is known as ENN: Equation with No Name
Derive the equation with no name
At any point along the path, a force -E must be exerted on the unit charge to hold it in equilibrium.
Where does capacitance exist?
Between any pair of conductors that are electrically insulated from one another
What is the capacitance equation?
Q = CV
What is the equation for the capacitance within a parallel plate capacitor with no dielectric?
C = Aε₀/d
Derive the equation C = Aε₀/d
What is the electric flux density around a capacitor (not between the plates)?
0
What is the equation for the capacitance within a parallel plate capacitor with a dielectric and air between the plates?
Where t₁ is the length of the air section and t₂ is the length of the dielectric section
Derive the equation
What is the definition of current?
the rate of change of charge through a fixed area with respect to time
What is the equation for the current, in terms of current density J, when the conductor has a uniform cross section?
I = current
J = current density
S = cross sectional area
What is the equation for the current, in terms of current density J, when the conductor has a non-uniform cross section?
I = current
J = current density
S = cross sectional area
What is the equation for current density in terms of charge density?
J = current density
ρᵥ = charge density
u = charge velocity
What is conductivity, σ?
Conductivity = 1 / Resistivity
σ = 1 / ρ
What is the equation for the force an electron experiences moving along a wire?
F = mu/τ = -eE
m = mass of electron
u = mean drift velocity
τ = average time between collisions of electrons
What is the equation for conductivity?
σ = conductivity
τ = average time between collisions of electrons
m = mass of an electron
e = fundamental charge
n = number of electrons
What is the equation for ohms law in terms of conductivity?
J = σE
what is j?
√(-1)
i is not used as it is used to represent an ac current
What is the equation for the AC impedance of a capacitor?
How does a capacitor behave when there is a DC current?
A capacitor blocks a DC current
What is the impedance of a capacitor when there is a DC current?
infinite
How does a capacitor behave when there is a AC current?
It passes AC currents
What is the equation for the potential difference across a charging capacitor?
Derive the equation for the potential difference across a charging capacitor
the green line separates a differential equation being solved
What is the equation for magnetic flux density surrounding a current carrying wire?
μ₀ = Permeability of free space
I = current in wire
r = radial distance from the wire
What is the equation for the electromagnetic force acting between two current carrying wires?
μ₀ = Permeability of free space
I = current in wire
r = radial distance from the wire
What are the units for magnetic flux density?
Tesla (T) or Weber per metre squared (Wb m⁻²)
What is the value of the Permeability of free space, μ₀?
4π x10⁻⁷
How is the electromagnetic force related to distance?
F ∝ 1/r
What is the Biot-Savart law?
a short element of wire of length dl carrying a current I produces a magnetic flux density δB at a position described by the vector r. The direction given by the cross product between the vector dl of the current in the wire at 1 and the position given by the vector r.
What is the equation for the Biot-Savart law?
r³ in the denomindator rather than r² as the r in the numerator is NOT a unit vector
What is the scalar form of the equation for the Biot-Savart law?
magnitude of dlxr = dlrsinθ, therefore r cancels to produce r² in the denominator
What is the right hand grip rule?
The magnetic flux density around long straight current carrying wire forms a set of concentric cicles centred on the axis of the wire. If you extend your thumb and curl your fingers and then align your thumb with the direction of the current, your curled fingers will indicate the direction of the magnetic flux density
Sketch the magnetic flux density around each of these current carrying wires and show the direction of the electromagnetic force acting on each of them:
Sketch the magnetic flux density around each of these current carrying wires and show the direction of the electromagnetic force acting on each of them:
Use the Biot-Savard law to derive the equation for magnetic flux density surrounding a current carrying wire?
What is the equation for the magnetic flux density on the axis of a wire loop?
Use the Biot-Savard law to derive the equation for magnetic flux density on the axis of a wire loop
What is the equation for the magnetic flux density inside a solenoid?
important
B = μ₀N₁I or B = μ₀N₂I/L
N₁ = Number of turns per unit length
N₂ = Number of turns total
What is the equation for magnetic flux, φ, when uniform lines of magnetic flux density flow normally across an element of area A?
φ = BA
What is the equation for magnetic flux, φ, when the magnetic flux density is not uniform across the area?
NOTE: Surface integral - NOT necessarily a double integral (but it can be)
What is “flux” in general?
The quantity of a field passing through an area
What is the equation for flux linkage?
flux linkage = Nφ
Usually φ = BA as it is commonly used for solenoids and inductors
What is Faraday’s law of electromagnetic induction?
The size of the induced electromotive force is proportional to the rate of change of the magnetic flux linking the circuit
What is Lenz’s law?
The direction or polarity of the emf generated by the change in flux was in the opposite direction such that it opposes the change in magnetic flux that caused it
What is the resulting equation from Faraday’s and Lenz’s law?
What is the self inductance of a circuit?
The ratio of the total magnetic flux linking the circuit over the current through the circuit generating the flux
What is the equation for the self inductance of a circuit?
L = φ/I
L = Inductance
φ = Total magnetic flux linking the circuit
I = Current through the circuit
What is the equation for inductance?
Henry (H)
What is the equation for Faraday’s law when including self-inductance?
What is the equation for the Inductance of an inductor?
Note: if N was the number of turns per unit length then the equation would not be divided by l
L = Inductance
μ₀ = Permeability of free space
μᵣ = Relative Permeability
N = Number of turns TOTAL
A = Area of loops
l = length of inductor
What is the difference between upper case V and I and lower case v and i?
V and v both represent voltage and I and i both represent current, however the upper case letters represent DC and lower case represent AC
What is the equation for the impedance of an inductor?
Z = jωL
How does an inductor react to AC and DC currents?
- It will pass a DC current
- It will block an AC current
