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EM Year 2 > Problems > Flashcards

Problems Flashcards

1
Q

Key point to find potential of shell from Gaus

A

Set integral limits r to infinity

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2
Q

2 key points to find charge from densities

A
  1. Integral is multiplied by charge density - rho, sigma etc
  2. Do not forget Jacobian
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3
Q

How to find charge for solid e.g. sphere of radius R

A
  1. Charge density, ρ = total charge/total volume
    = q/ 4 π/3 R^3

Or Q = ρ V

  1. Qenc = Q * (Volume inside Gaussian/volume inside sphere)
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4
Q

What must you always remember when stating the field

A

Unit vector

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5
Q

Energy formula for particles

A
  • Total energy = K.E. A + K.E.B + Coulomb
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6
Q

How to find simultaneous equations to solve for energy problems

A
  1. conservation of energy
  2. Conservation of momentum
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7
Q

Radius used for dA in Gauss Law

A

Gaussian surface - usually r

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8
Q

Radius used for charge

A

Small r inside shape

Big r outside shape

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9
Q

Formula for energy stored in assembling spherical shell

A

W = 1/2 * εo ∫ σ dA

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10
Q

Surface area of cone

A

πrS + πr^2

***S = slant height, not perpendicular height

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11
Q

Steps to find potential difference of unusual shape

A
  1. Find potentials separately
  2. State potential equation; V = k ∫q/curly r
  3. Use diagram to define curly r, r and r’
  4. Find curly r in terms of unit vectors - consider change in coordinates
  5. Find magnitude of curly r
    6.Define da in terms of coordinates
  6. Use diagram to simply any terms
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12
Q

Using curly R method to find potential or field at a distance from SOLID

A
  • Take a slice and reduce to area integral
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13
Q

How to find monopole moment

A

Sum of magnitude of charges

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14
Q

How to find dipole moment

A

∑QiRi
* WITH UNIT VECTORS

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15
Q

Potential at large r from pole moments

A

Potential = ∑pole = Vmonopole + Vdipole etc (kQ/r)

  • Use Q = Qtotal for monopole and Q = p.r for dipole
  • May need theta for dot product for latter e.g. 3qa Rhat.Z hat -> 3qa cos θ
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16
Q

Force formula

A

QE

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17
Q

Work formula

A

= qV

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18
Q
A
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19
Q

Pattern of potential inside a conductor

A

Uniform

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20
Q

Separation vector

A

From source to observer

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21
Q

Calculate potential across changing E fields

A

= -kQ/ r

BUT different integral limits according to differing E fields

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22
Q

Meaning a grounding wire making a shell’s potential = 0

A

Enclosed E field =0

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23
Q

Capacitance from Electric field

A
  • Gauss to find E field
  • Inegrate to find potential
  • C = Q/V
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24
Q

What to remember for bound surface and volume charges

A
  • Need conversion to spherical coordinates (or others if appropriate)
25
Formula for bound volume charge
ρb = - ∇.P **unit vectors and coordinate conversions
26
Formula for bound surface charge
σb = p.n =p cos \\\\\\\\\\\\\\\\\\\]’ **unit vectors and coordinate conversions
27
Volume bound charge if P is uniform
Zero
28
If put dielectric in eternal field Eext and it polarises (E induced), what is E total?
Eext + E induced
29
Electric field outside a volume with surface and volume charges (2 considerations)
1. Q = Volume x volume charges + volume x surface charges 2. Gaussian surface inside volume - sigma for charge Gaussian surface outside volume - sigma and Rho for charge
30
How to substitute in unit vector e.g. for dipole
- r = l r l X R hat
31
Consideration asked to find electric field after volume/surface charge
- Sub in values for charges (remove sigma/rho)
32
Electric field
33
Gauss’ Law for Dielectrics
∇ . D = ρfree D= displacement field
34
Which charges form displacement field?
Free charges
35
Which charges for external electric field?
Free charges
36
Define electric susceptibility
χe - how easily a material becomes polarized when placed in an electric field
37
Linear dielectric formula
P = ε 0χeE
38
Displacement field formula
D = ε 0E+ P (where P = eoXoE)
39
Formula relating free charge to displament field
∫D. Da = Q free, enclosed
40
Features of bound charge (3)
- Arise from a material’s internal structure or dipoles - Result from polarisation - Can be measured and controlled
41
Best displacement field formula for known free surface charge Q
D = Q/A (n hat)
42
Best displacement field formula for known volume charge ρfree
∇ . D = ρfree
43
Best displacement field formula for known polarisation and electric field
D = ε E + P
44
Best displacement field formula for linear material
εE
45
Where are electric fields discontinuous?
- Boundary of surface of conductor and normal to surface - free charges
46
Charge density from electric field
∇.E = ρ / εo
47
Where are displacement fields discontinuous?
- At boundaries
48
Epsilon, ε , inside dielectric
ε = εo ( 1 + χ)
49
∇ (r hat/ r^2)
- 4 π δ^3 r
50
Electric field inside uniformly polarized sphere
E inside = - P/ (3 εo)
51
Relation of electric field to polarisation
Uniform and opposite to polarisation direction
52
diamagnetic
Create weak opposing magnetic field when exposed to external field - weak repulsion
53
Paramagnetic
Create weak aligned magnetic field in external magnetic field
54
Ferromagnetic
Permanent magnetisation Create strong aligned magnetic fields, even without external magnetic field
55
Relate electrons to dia- para- and ferro- magnetic
- D: Paired electrons, small induced moment - P: Unpaired electrons - F: Unpaired electrons - collective coupling in unpaired spin
56
Relate magnetic susceptibility to dia- para- and ferro- magnetic
- D: χm <0 - P: χm > 0 but <<<1 - F: χm >>1 (large and positive)
57
Differential equation for current and current density
- dI = J x surface area dr
58
RHR for lorentz
Same as equation F = v x B - Force - Velocity - B fields
59
Steps to find force on wire in magnetic field
1. Draw 2. F = I ∫ dl x B (cross product) 3. Write out with unit vectors 4. Find cross product of unit vectors 5. If given values for B or I in terms of coordinates sub in values e..g looking at line at x=-2 and B = kx, B= -2k 6. Integrate 7. UNIT VECTORS

EM Year 2 (10 decks)

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