Week 2

Question 1

What is retardation?

Answer 1

Delay in the movement of charge being felt by another

Question 2

What does curly r represent?

Answer 2

Separation vector: r - r’

Question 3

What is the net force acting on a charge in words?

Answer 3

The vector sum of the forces caused by every other charge in the universe

Question 4

What is force in terms of electric fields?

Answer 4

F = QE

Question 5

How do equations change for considering continuous distribution instead of point charge?

Answer 5

Integration

Question 6

Formula for electric fields of continuous charge distribution

Answer 6

E ( r ) = (1/ (4 PI Eo) * volume integral ( rho (r’) / curly r^2 ) * curly r hat d Tau’

Question 7

Formula for electric field of point charge

Answer 7

AKA coulomb law

E(r) = 1/ (4piEo) * q/ curly r^2 * curly r hat

Question 8

What is dq for a line?

Answer 8

λdl

Question 9

What is dq for surface?

Answer 9

σda

Question 10

What is dq for a volume?

Answer 10

ρ d τ

Question 11

How to turn general case into specific dimension?

Answer 11

Dirac delta

Question 12

Where do electrostatic lines start and finish?

Answer 12

Start as positive, end at negative or infinity

Question 13

How does is flux arranged in flux tubes?

Answer 13

Constant through every cross-section of the tube

Question 14

By what proportion does the CSA of flux tubes grow?

Answer 14

R^2

Question 15

By what proportion does flux density in tubes change and why?

Answer 15

1/r^2 to compensate for increasing area

Question 16

What are inward flowing flux tubes?

Answer 16

Negative flux

Question 17

What are outward flowing flux tubes?

Answer 17

positive

Question 18

What is net flux through a closed surface proportional to?

Answer 18

Total charge( positive - negative) inside the volume enclosed by the surface
- Intregral form of Gauss

Question 19

How to obtain differential form of Gauss from integral?

Answer 19

Sub in:
- RHS: Divergence theorem -> Flux = Volume integral of divergence of field
- LHS: Q enc = volume integral of ρ d τ

Question 20

What does Gauss law in differential form tell us?

Answer 20

Divergence of electric field is proportional to the volumetric charge density at every point in space

Question 21

What is the Gaussian surface for spherical symmetry?

Answer 21

Concentric sphere of varying radius

Question 22

What is the Gaussian surface for cylindrical symmetry?

Answer 22

Coaxial cylinder of varying radius s, arbitrary length l

Question 23

What is the Gaussian surface for plane symmetry?

Answer 23

Gaussian pillbox (rectangular cuboid) that straddles the surface

E.da = [Ez Z1 - Ez Z2]

Question 24

When does Gauss become less useful?

Answer 24

When symmetry is broken

Question 25

What is special about an irrotational field?

Answer 25

It can be written as the gradient of a scalar potential field because it derives from a scalar potential (V)

Question 26

Which 2 statements are implied from an irrotational field?

Answer 26

E = - ∇ V V (b) - V (a) = - ∫ E . Dl

Question 27

What is the reference point for V (r)?

Answer 27

Technically a difference between 2 points - typically set r to infinity so V(r) = 0

Question 28

What is the formula for potential of a point charge?

Answer 28

V = 1/ (4 * pi * Eo) = q/ curly r

Question 29

What is r?

Answer 29

Vector from origin to source

Question 30

What is r’?

Answer 30

Vector from origin to test charge

Question 31

What is electric field definition?

Answer 31

Force per unit charge as if a test charge was placed at that point

Question 32

What is superposition?

Answer 32

When forces/fields are added vectorial

Question 33

How to depict Dirac delta for a plane?

Answer 33

E(r) = ∫ ∫ 1/ (4 * pi* Eo) * ρ d T / (curly r^2) * curly r hat E(r) = ∫ ∫ 1/ (4 * pi* Eo) * σ δ(z) dxdydz / (curly r^2) * curly r hat E (r) = 1/ (4 * pi* Eo) * ∫ δ(z) dz ∫ ∫ σ dxdydz / (curly r^2) * curly r hat - where δ(z) dz = 1

Question 34

What is the work to move test charge?

Answer 34

V (b) - V (a) = W/Q

Question 35

What is the work to assemble charge distribution

Answer 35

W = Eo/2 ∫ ∫ ∫ [E] ^2 d τ

Question 36

Units for potential

Answer 36

NM/C or J/C

Question 37

Name and value for Eo

Answer 37

Permittivity of free space = 8.85 * 10 ^-12 c^2/ NM^2

Question 38

What is the sign convention for potential and charges?

Answer 38

Positive for positive charge as work is needed to bring test charge closer

Question 39

What is the work bringing an isolated charge from infinity to isolated area/

Answer 39

0 as no other charges exist to exert a force

Question 40

What is the total work to move numerous charges?

Answer 40

Qi (1st charge moved ) * sum of potential for each individual charge

Question 41

What does work to assemble configuration of point charges represent?

Answer 41

Energy stored in configuration, amount of work you would get back on dismantling the system

Question 42

What is the formula for energy of a continuous charge distribution?

Answer 42

W = 1/2 ∫ ∫ ∫ ρV d τ = Eo/2 ∫ ∫ ∫ [E]^2 d τ —> form substitution Gauss Law and ∇ V = -E

Question 43

What is a dipole?

Answer 43

Two equal and opposite charges separated by vector d

Question 44

What is the direction of vector d in dipole?

Answer 44

Negative to positive

Question 45

What is the formula for superposition of dipole

Answer 45

V (r) = 1/ (4 * PI * Eo) (q/r+ - q/r-) = q/(4 *pi * Eo) * (r- - r+)/(r+r-)

Question 46

What happens to V dipole at long distances? I.e r>>d

Answer 46

- r- -r+ ~ d cos θ and r+r- ~ r^2 V (r) = 1/ (4 * PI * Eo) (q d cos θ) / r^2 Where r= curly r

Question 47

What is the vector dipole moment?

Answer 47

P = q d = q d dhat V (r) = 1/ (4 * PI * Eo) (r hat . P) / r^2

Question 48

What is the difference between potentials of a dipole compared to point charge?

Answer 48

- Dipole decreases by 1/r^2 - Point charge decreases by 1/r

Question 49

How to arrive at idealised point dipole?

Answer 49

decrease distance d to 0 and increase q to infinity to keep p constant p = qd

Question 50

When do Q and d cease to be important?

Answer 50

When d<<

Question 51

When does dipole become relevant?

Answer 51

When monopole term = 0 Total charge often 0 as positive and negative terms like to pair up - if monopole = 0 , dipole dominates

Question 52

What is the dipole moment for a collection of charges?

Answer 52

P = ∑ ri . Qi

Question 53

What is the dipole for charge distribution?

Answer 53

P = ∫ ∫ ∫ r ρ d τ

Question 54

What s the charge for a collection of point charges in a momopole?

Answer 54

Q tot = ∑ qi

Question 55

What is the charge for charge distribution in a monopole?

Answer 55

Q total = ∫ ∫ ∫ ρ d τ

Question 56

How to derive equation for physical dipole with 2 charges?

Answer 56

P = ∑ ri . Qi - Diagram showing r1-r2 = d, where q1=-q2 P = r1q1 + r2q2 = q (r1 - r2) = qd

Question 57

Point charge from charge distribution

Answer 57

Q tot = ∫ dq = ∫ ∫ ∫ ρ δ^3 (r)

Question 58

Point charge from charge distribution

Answer 58

Q tot = ∫ dq = ∫ ∫ ∫ ρ δ^3 (r)

Question 59

Most important when finding enclosed charge with volume integral

Answer 59

JACOBIAN!!

Question 60

Charge for infinite plates

Answer 60

σ A

Question 61

Enclosed charge from charge density

Answer 61

Q tot = ∫ dq = ∫ ∫ ∫ ρ δ τ

Question 62

Limits for charge integral when hollow surface

Answer 62

Radius of inner surface of conductor to gaussian (e.g. a to r)

Question 63

Important fact about potential inside a solid sphere

Answer 63

Does not equal 0 - split integral into.2 parts

Question 64

Charge enclosed in solid sphere

Answer 64

1. ρ = Q/V. ——> Q = ρ/V

Question 65

Which radius to use for charge of solid?

Answer 65

R - radius of sphere

Question 66

Which radius to use for area?

Answer 66

Small r - variable, or Gaussian surface radius

Question 67

Poison equation

Answer 67

∇^2 V = - ρ/ Eo

Question 68

Laplace Equation

Answer 68

∇^2 V = 0