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MS1 > Electromagnetism > Flashcards

Electromagnetism Flashcards

1
Q

Equation for current.

A

I = dq/dt

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2
Q

Coulomb’s law.

A

F = k Q1Q2/(r^2)

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3
Q

How does Coulomb’s law change for vector?

A

Multiply by vector r^

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4
Q

How can the force on a charge be found from two close point charges?

A

Using superposition principle.

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5
Q

Equation for electric field.

A

E=F/q

E and F are vectors.

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6
Q

How can electric fields from point charges be combined?

A

Using superposition principle.

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7
Q

Dipole moment equation

A

p=qa

p is vector
a is vector from negative to positive

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8
Q

Derive equations for electric field parallel and perpendicular to the dipole axis.

A

Check derivation.

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9
Q

Derive equation for electric field of a dipole in a general position.

A

Check derivation.

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10
Q

By superposition, derive the field from an infinite plane of uniform charge distribution.

A

Check derivation.

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11
Q

Flux equation

A

Flux = ∫E.dS

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12
Q

Gauss’s Theorem

A

Sum(charge)/ε0 = ∫E.dS

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13
Q

Easy geometries for Gauss’s Theorem

A

Field perpendicular to surface and same value at all positions on surface.
Field parallel to surface (E.dS=0)

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14
Q

Work done moving charge in electric field

A

W=-q ∫E.dl

As dW=F.dl
and F=-qE when external force is applied

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15
Q

Work done moving charge through closed loop

A

=0

Due to conservative nature of electric field

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16
Q

Derive an expression for potential energy of a dipole in an E-field.

A

Check derivation

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17
Q

How can the potential from two point charges be found?

A

Using superposition.

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18
Q

How to find E from V?

A

Partially differentiate V to give E in a certain direction.

E=-gradV

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19
Q

How are equipotentials distributed in a conductor?

A

There is no potential difference in a conductor thus a conductor carrying static charge is an equipotential volume with an equipotential surface.

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20
Q

Definition of capacitance.

A

Ratio of charge to potential

q=CV

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21
Q

Energy stored in a capacitor equation.

A

dW=Vdq

W = ∫Vdq = QV/2

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22
Q

Equation for εr

A

εr=Cd/C0

Capacitence with dielectric to capacitance without.

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23
Q

Define electric polarisation

A

Dipole moment per unit volume

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24
Q

Total E field in presence of dielectric

A

E=E0+Ep

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25
Q

In isotropic materials, equation relating polaristation and field.

A

P=ε0χE

χ is electric susceptibility.

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26
Q

Derive relationship between dielectric constant and susceptibility.

A

Check derivation

Result
εr=1+χ

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27
Q

Gauss’s Law in presence of a dielectric

A

∫E.dS=sum qc/ε0 + sum qp/ε0

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28
Q

Derive D = ε0E+P

A

Check derivation

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29
Q

Derive D = ε0εrE

A

Check derivation

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30
Q

Derive boundary conditions for an electric field.

A

Check derivation

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31
Q

Derive boundary conditions for electric displacement.

A

Check derivation

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32
Q

What are piezoelectrics?

A

Materials that exhibit electric polarisation under the influence of applied mechanical stress.

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33
Q

What are pyroelectrics?

A

Materials in which the electric polarisation can be modified by changing temperature.

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34
Q

What are ferroelectrics?

A

Non-linear dielectric materials with spontaneous polarisation that can be controlled and reversed by the application of an electric field.

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35
Q

What is a necessary condition of piezoelectrics, pyroelectrics and ferroelectrics?

A

The crystal structures do not contain a centre of symmetry.

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36
Q

Piezoelectric effect expressed in two equations.

A

P = qZ+χε0E
P is polaristaion, q is piezoelectric coefficient, Z is stress, χ is electric susceptibility, E is electric field.

e = sZ+qE
e is strain and S is compliance

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37
Q

Why must a material be a single crystal for it to display piezoelectric effects?

A

In a polycrystalline material the dipoles will cancel.

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38
Q

Equation for pyroelec tric coefficient.

A

p=dPs/dT

p is pyroelectric coefficient, Ps is spontaneous polarisation and T is temperature.

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39
Q

Applications of pyroelectrics.

A 
Temperature sensors (though unreliable due to air)
Detectors and infra red imaging devices.
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40
Q

Derive the condition for the ferroelectric state to be achieved from the ferroelectric catastrophe.

A

Check derivation

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41
Q

Area inside a ferroelectric hysteresis loop.

A

Is equal to the energy disipated.

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42
Q

Current in terms of current density equation.

A

I=∫J.dS

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43
Q

Define current density.

A

Charge oer unit time crossing a unit area of surface which is perpendicular to the direction of motion.

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44
Q

Derive I=-neAv by differentiation and hence derive J.

A

Check derivation.

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45
Q

Show that resistance is proportional to length.

A

Check derivation.

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46
Q

Show that resistance is inversely proportional to area.

A

Check derivation.

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47
Q

Microscopic form of Ohm’s law

A

J=σE

E=ρJ

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48
Q

Derive R=ρl/A for a one dimensional current flow through wire length l and CSA=A

A

Check derivation

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49
Q

Derive power disipated for a small charge dq being taken through a potential V in time dt.

A

Check derivation

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50
Q

State the assumptions of the Drude model.

A

Electrons are a ‘gas’
Electrons are only scattered by collisions with ionic cores
Electrons do not interact with each other or ions
The average time between collisions is τ with probability of scattering per unit time of 1/τ.

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51
Q

Derive σ using the Drude model

A

Check derivation

52
Q

Strengths of the Drude model.

A

Accurately opredicts average scattering distance.

53
Q

Weaknesses of the Drude model.

A

Underestimates electron velocities and can’t accurately predict thermal conductivities or Cp.
Does not use quantum mechanical model.

54
Q

Two main consequences for practical applications of superconductors.

A

Currents generated in superconducting wires do not need a power supply to keep them going.
Currents in superconductors do not generate hear, meaning higher current densities can be maintained compared to normal wires.

55
Q

State Kirchoff’s first law.

A

The algebraic sum of the currents meeting at a junction equals zero.

56
Q

State Kirchoff’s second law

A

The algebraic sum of potential differences around a closed path in the circuit equals the EMF along the path.

57
Q

Derive the equation for an unknown resistance of resistor in a Wheatstone bridge.

A

Check derivation

58
Q

Derive F=IdlxB

A

Check derivation

59
Q

Derive Lorentz force on charge q.

A

Check derivation

60
Q

Equation for magnetic dipole moment of a bar magnet

A

m=qA

q is pole strength.

61
Q

Equation for magnetic dipole moment if a current loop

A

dm=IdA

m=IA

62
Q

By considering force on a rectangular current loop, derive an expression for the torque acting on the loop.

A

Check derivation

63
Q

State the Biot-Savart Law

A

Check

64
Q

Use Biot-Savart Law to derive magnetic field around a straight wire carrying steady current.

A

Check derivation

65
Q

Use Biot-Savart Law to derive magnetic field along axiz of a circular loop.

A

Check derivation

66
Q

Use Biot-Savart Law to derive magnetic field along the axis of a solenoid

A

Check derivation

67
Q

Equation for force between two monopoles.

A

F = (μ0q^2)/(4πr^2)

68
Q

Equation for magnetic field around a monopole.

A

B = (μ0q)/(4πr^2)

69
Q

Work doen in moving a monopole in a magnetic field B a distance dl.

A

dW=B.dl

70
Q

Is a magnetic field conservative?

A

No, meaning W=∫B.dl≠0

71
Q

State Ampere’s law

A

The work done in taking a unit monopole around a closed path is equal to μ0 times the current threading the path.

72
Q

Ampere’s law equation

A

∫B.dl = μ0I

73
Q

Use Ampere’s law to find the magnetic field due to a solenoid.

A

Check derivation

74
Q

Use Ampere’s law to find the magnetic field due to a toroidal coil.

A

Check derivation

75
Q

Definition of magnetic flux

A

Amount of magnetic field crossing a given surface.

76
Q

Equation for flux

A

Φ =B.A

77
Q

Gauss’s theorem for a B field.

A

∫B.dS = 0

The flux of B over a closed surface is zero.

78
Q

Why is the flux of B over a closed surface zero?

A

A magnetic monopole cannot be isolated.

79
Q

State Faraday’s Law

A

Induced emf depends on rate of change of flux

80
Q

Lenz’s law equation

A

EMF = dΦ/dt

81
Q

State Lenz’s law

A

Wherever a change in flux induces a current, the direction of the current flow is such as to oppose the change that caused it.

82
Q

Derive Faraday’s law from force on a moving charge moving at velocity v in a field strength B.

A

Check derivation

83
Q

Equation for self inductance

A

Φ=LI

84
Q

Definition of self inductance

A

The magnetic flux passing through a circuit when a unit current flows in it.

85
Q

Derive the self inductance in a long solenoid.

A

Check derivation

86
Q

What is mutual inductance?

A

Where two circuits are close to one another and flux from one influences the other and vice versa.

87
Q

Find the mutual inductance in two coils of same radius with different numbers of turns.

A

Check derivation

88
Q

Equation linking mutual inductance and self inductance in transformer.

A

M^2=L1*L2

Not gernally applicable, if circuits moved apart then M^2

89
Q

Equation for relative permeability of an inductor with a magnetic material present Lm.

A

Lm/L0=μr

90
Q

Relate B and H using μr and μ0

A

B=μrμ0H

91
Q

Relate B to H and M

A

B=μ0(H+M)

Where M is magnetic moment per unit volume (megnetisation).

92
Q

Relate M and H.

A

M=χmH

χm is magnetic susceptibility

93
Q

What are the boundary conditions for magnetostatics?

A

B1 perp = B2 perp

H1 para = H2 para

94
Q

Potential energy for a magnetic dipole in a B field.

A

U = -m.B

negative sign due to dipole lowering energy as it aligns with field direction.

95
Q

What is a diamagnetic material?

A

A material with no permanent dipole moments on the atoms.

96
Q

What happens when a diamagnetic material is placed in a magnetic field?

A

EM induction takes place and the electrons orbit nucleus to generate an opposing magnetic field. This effect is weak so diamegnetic materials have small χ values.

97
Q

For a diamagnetic material’s χ value vary with temperature?

A

Not significantly.

98
Q

A superconductor has a χ value equal to what?

A

χ=1

as perfect diamagnet.

99
Q

What is a paramagenetic material?

A

A material in which permanent dipole moments exist from electron spin but the dipoles are randomly arranegd so in the absence of a magnetic field there is no magnetisation.

100
Q

What happens when a magnetic field is applied to a paramagentic material?

A

The dipoles tend to align in the same direction as the applied field to lower their energy.

101
Q

What kinds of χ values do paramagnetic materials have?

A

Small positive χ values.

102
Q

How does χ vary with temperature for a paramagnetic material?

A

χ = C/T

C is a positive constant

103
Q

What is a ferromagnetic material?

A

A material where below a critical temperature, neighbouring atoms interact (exchange interaction) causing magnetic moments to align parallel to one another. This is spontaneous magnetisation (magnetisation without an external applied field).

104
Q

What is a Curie temperature for a ferromagnet?

A

The temperature below which the material displays ferromagnetic properties.

105
Q

How does a ferromagnetic material behave above the Curie temperature?

A

Like a paramagnetic material.

106
Q

How does χ vary with T for a ferromagnetic material?

A

χ = C/(T-θc)

107
Q

Applications for ferromagnetic materials.

A

Electromagnets
Motors
Transformers
Generators

108
Q

What is a soft magnetic material?

A

A material with a low remnent magnitisation.
Small hysteresis loop.
Iron

109
Q

Applications of soft ferromagnets.

A 
Electromagnet
Transformer core (response to applied field)
110
Q

What is a hard magnetic material?

A

A material with a large remanent magnitisation.

111
Q

Applications of hard magnetic materials.

A

Permanent magnet applications such as magnetic hard disks where bits are magnetised such that the domain can be pointing in either direction (±Mr) and retain the magentisation so it can be read.

112
Q

First Maxwell equation is based on which law?

A

Faraday’s law.

113
Q

Derive the first Maxwell Equation

A

Check derivation

114
Q

Second Maxwell equation is based on which law?

A

Gauss’s Law

115
Q

Derive the second Maxwell equation

A

Check derivation

116
Q

Third Maxwell equation is based on what relation?

A

Magnetic flux through a surface equals zero.

117
Q

How to resolve Ampere’s Law paradox for a capacitor.

A

Replace I with sum of conduction and displacement currents.

118
Q

Fourth Maxwell equation is based on which law?

A

Ampere’s Law

119
Q

Write fourth Maxwell Equation

A

Check.

120
Q

What is the speed of light in terms of constants?

A

c=sqrt(μ0ε0)

121
Q

Speed of light in medium with εr and μr?

A

c’=sqrt(μrμ0εrε0)

122
Q

Refractive index in a medium in terms of εr and μr?

A

n = c/c’ = sqrt(μrεr)

123
Q

If a metamaterials was to be engineered to have a negative εr and negative μr leading to a negative refractive index, what properties would it have?

A

Reflection rather than transmission of light casuing invisibility.

124
Q

Skin depth equation for a conductor in an electric field.

A

E = E0 exp(-z/δ)

where
δ is skin depth
z is distance of charge from surface

125
Q

Skin depth for a good conductor

A

δ = sqrt(2/(ωμσ))

ω is frequency
μ is magnetic permeability
σ is conductivity

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