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EM Year 2 > Week 3 > Flashcards

Week 3 Flashcards

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1
Q

How are conduction electrons positioned?

A
  • Sea surrounding positive ions
  • Positioned to ensure electric field inside conductor is zero at every point
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2
Q

What do we assume about conductors?

A

Perfect with unlimited supply of free charge

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3
Q

When is force exerted on charges

A

With unlimited free charge until static equilibrium reached

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4
Q

What is the electric field at equilibrium in a perfect conductor?

A

Net field inside = 0

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5
Q

What is charge density inside a conductor and why?

A

ρ = 0 from Gauss’ Law

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6
Q

Where do net charges reside in a conductor and why?

A

On the surface

  • Gauss law means they create a field which is felt outside and cancels net internal E field
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7
Q

What is the potential for conductors and why?

A

V(r) = constant

Any path through inside will have E=0along all points

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8
Q

What is the orientation of the E field?

A

Perpendicular (tangential would mean charges move along surface)

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9
Q

Define floating conductors

A

Isolated, not connected to anything so charge cannot flow in or out of them

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10
Q

What is the value and distribution of charge in floating conductors?

A
  • Fixed total net charge as cannot flow in or out of them ( neutral (Q=0) or isolated)
  • can be redistributed to maintain E = 0
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11
Q

What is the potential in a floating conductor?

A

Variable depending on changes in charge distribution to maintain E = 0

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12
Q

What is the value and distribution of charge in fixed conductors?

A
  • Connected to potential source +/- earthed or grounded
  • Varies as need to maintain fixed potential and E = 0 inside
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13
Q

Define induced charge

A

A charge that appears on a surface when a charge is moved closed to a conductor to maintain equilibrium

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14
Q

How do induced charges differ in grounded and floating conductors?

A

Floating = if negative is induced on one surface, positive induced on opposite so total net charge =0

Grounded = if negative is induced on one surface, voltage source can correct for this

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15
Q

What is the criteria for Gaussian surface inside conductors?

A

Must have zero flux so it has zero net charge inside

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16
Q

What is the electric field vector?

A

E (r) = σ (r) / εo

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17
Q

Differential potential equation

A

V = - ∫ E.dl

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18
Q

Define capacitance

A

Constant of proportionality between charge and potential difference

C = Q/V

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19
Q

What does capacitance depend on?

A

Geometry of conductors (size, shape, separation)

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20
Q

What are the types of induced dipoles in matter

A
  • Atomic polarisation
  • ionic polarisation
  • Molecule polarisation
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21
Q

Describe atomic polarisation

A
  • Neutral atoms
  • Electric field creates a polarisation (dipol
  • Electron cloud displacede) and becomes a conductor
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22
Q

Formula for induced dipole

A

P= α E

α = atomic polarisability

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23
Q

What does α depend on?

Study These Flashcards
A

Detailed structure of atom

Also α = εo χo ( perm vs electric susceptibility)

24
Q

What makes up dipole forces?

Study These Flashcards
A
  • Electric field pushes apart
  • Mutual attraction of dipoles pulls together
25
Describe ionic polarisation
- For dielectrics made of lattice of ions - Lattice displaced - External electric field -> small displacement between sublattices causing electric dipoles
26
Describe molecule polarisation
- Polar molecules aligned - Have pre-existing permanent dipoles (polar) but net moment usually zero - In electric field positive and negative experience different forces creating torque to align dipole to E
27
Formula for permanent dipole
P = qd
28
Formula for torque from external field on permanent dipole
N = p cross E
29
What causes a dielectric to become polarised?
Applied electric field
30
What is the dipole moment per unit volume?
P (r) = n . P (N molecules per unit volume each with a dipole p)
31
What are bound charges?
Those bound to an atom or molecule and unable to move freely
32
Formula for surface bound charges
σ = P.n - maximal when parallel, 0 when orthogonal
33
What is the orientation of uniform surface bound charges?
- 2 opposite edges polarised due to accumulation of charge - p = 0 centrally - n hat points out from other edges
34
Formula for volumetric bound charges
ρ = - ∇. P
35
What is the orientation for non-uniform volumetric bound charges
Radial, with negative accumulation at centre
36
Formula for total charge
ρ = ρ free + ρ bound - free = controlled in experiement e.g. set potential ( ∇ .E = ρfree/ εo) - bound = appear in dielectrics due to polarisation
37
Derivation of macroscopic Gauss Law equation
1. Gauss Law 2. Sub in ρ = ρf + ρb 3. Sub in ρb = - ∇.P 4. Rearrange for ρf 5.Factor out ∇ 6. Sub in D = εoE + P
38
Differential form of macroscopic Gauss Law
∇.D = ρf
39
Integral form of macroscopic Gauss Law
∫ ∫ D.da = Qfree enc (via divergence theorem)
40
Why is D not εoEfree?
(May assume as ∇.Ef = ρf/ε and ∇.D = ρf - Although same divergence as Efree, curl is different so different fields ∇ x E free = 0 ∇ x D = 0 + ∇ x P
41
Why are displacement fields useful?
- Simplify the analysis of electric fields in materials that are not perfect conductors (like dielectrics). - The displacement field accounts for both free charges and bound charges in a material. - It separates the effects of free charges from the material’s response (polarization), making it easier to apply Gauss's Law in different media.
42
Define electric susceptibility
measures how much a material becomes polarized in response to an applied electric field
43
What are linear dielectrics
- materials where the polarization is directly proportional to the applied electric field. - the relationship between the electric field E and the polarization P is linear, meaning that the material’s ability to polarize doesn’t change with the strength of the electric field
44
Displacement field formula
D = εo (1 + χo) E
45
When do volumetric bound charges appear?
Inside volume of a dielectric when P and a non-zero divergence
46
How to calculate field ?wihtin a material?
once found bound charges, can ignore polarisation vector P and calculate field from bound charges and any external or free charges
47
What are the bund charges for. Uniformly polarised sphere, with constant polarisation P throughout
- Bound volumetric= 0 as divergenceless - Bound surface = P. N hat
48
What is the electric field for 2 spheres of opposite charge, slightly offset?
E = Esph1 + Esph2 = (ρ /3εo )( r- r+) - (ρ/ 3εo) (r - r-) = - (ρ/ 3εo) (r+ - r-) = - ρd/ 3εo = - P/ 3εo
49
What does the result for electric field inside a sphere tell us
- Inside is a uniformly polarised sphere independent of position - field produced by bound charges is constant inside p here and opposite to polarisation - field outside corresponds to that of a physical dipole
50
51
What is relative permittivity
dielectric constant, is a measure of how much a material can store electrical energy in an electric field compared to a vacuum = 1+ χo
52
How do electric and displacement fields differ at interfaces of mediums with different permittivity
- electric field E can change at the interface of different materials because it depends on the material's permittivity - displacement field D is continuous across the interface when there are no free surface charges.
53
When is D proportional to E?
Only inside linear dielectric
54
What is the dielectric’s effect on capacitance?
- increases the capacitance of a capacitor by a factor of εr - because bound charges act like tiny dipoles and create their own electric field that opposes the original electric field - so reducing the electric field inside the capacitor for a given charge
55

EM Year 2 (10 decks)

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