Week 6 Flashcards

1
Q

Magnetic part of Lorentz force law

A

Magnetism analogue of Coloumb’s law

Which is force on test charge Q, moving with velocity v in magnetic field B

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2
Q

Why are the velocities in magnetostatics?

A

The movement of charges causes a static magnetic field (unchanging magnetic field)

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3
Q

Right hand rule

A

For cross product eg V x B

First point thumb in direction of V, then index finger in direction of B

Resultantly middle finger points in direction of cross prod vector

Each subsequent finger is orthogonal

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4
Q

Lorentz force law

A
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5
Q

Prove that the force on a closed loop of wire carrying current I due to a constant magnetic field B is zero

A
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6
Q

The size of force due to a magnetic field is?

A

Where α is the angle in between v and B

The field B produces no force on the static test charge Q
Therefore the size of force depends only on |v|Sinα

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7
Q

Interesting consequence of force law

A

Direction of force depends on sign of charge

You can tell the charge of a particle by seeing which direction it is deflected in when moving through a magnetic field

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8
Q

Magnetic forces and work

A

Fmagnetic is perpendicular to v therefore force due to magnetic field does not do any work as

Fmagnetic • dl = Fmagneticvdt = 0

Magnetic forces can’t accelerate a charged particle, only alter direction that test charges move

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9
Q

A current is

A

A charge in motion

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10
Q

Units for current

A

1 Ampere = 1 coulomb per second

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11
Q

Current vector points

A

In the direction opposite to the movement of electrons

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12
Q

Calculate Fmagnetic for charge density λ and on a length of wire

A
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13
Q

Define the magnetic force on a surface

A
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14
Q

Define a magnetic force through a volume

A
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15
Q

Derive the continuity equation

A

Taking the volume current density (which ishow much charge flows through a surface area element):
J • da = ρvCos(θ)da

Which then in time is ρ(vCos(θ)dt)da then

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16
Q

Steady current

A

No build up of charge

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17
Q

Assumptions of electrostatics and magnetostatics

A

accordingly

stationary charge
steady current

18
Q

Significance of?

A

This is a consequence of working with magnetostatics

This means the field lines of J can’t begin or end on any local point (compare to grad • E = ρ/ε0 in electro case where electric field lines can begin or end on any charges which give rise to nonzero value of ρ)

19
Q

Biot Savart rule

A

Physical rule that governs how steady currents in wires produce static magnetic fields

Where:
I = Idl’ for a current wire
P is path along wire
s = r - r’

20
Q

μ0 ?

A

4π * 10**-7

21
Q

Right hand rule for magnetic field

A

If you wrap your hand around a wire such that your thumb is pointing in the direction of flow of the current through that wire (up or down) then

The direction that your fingers curl around the wire represent that direction of flow of the magnetic field at some arbitrarily close distance

22
Q

Trig substitutions

A
23
Q

Sin rule

A
24
Q

Cosine rule

A
25
Q

Angular basis vector in cylindrical coordinates

A
26
Q

Find magnetic field at a fixed distance ρ from an infinite straight wire on the z axis carrying steady current I travelling up in z direction

A

Where r is a point at radial distance ρ from the wire

27
Q

When does a charge NOT contribute to the flux integral of an electric field

A

When the charge is located outside of the surface being integrated over

28
Q

When does a current not contribute to the line integral of a closed path

A

When the path doesn’t enclose the wire

29
Q

Show the curl of B around the infinitely long straight wire coinciding with z axis

A
30
Q

Deduce that

A

Given that rhs of stokes theorem = μ0*I P

31
Q

State Biot Savart law in terms of volume current density J

A
32
Q

Use Biot Savart to deduce

A
33
Q

Derive Ampere’s law

A
34
Q

Magnetic field as of an infinite charged plane

A

Where K is the uniform surface current

35
Q

Motivate the vector potential

A

Given M3, it would be sufficient to show that B can be given as a curl of a vector field

This is because the divergence of the curl = 0

36
Q

Find Kronecker deltas from epsilon tensors

A
37
Q

Laplacian in components

A
38
Q

Is magnetic potential uniquely defined

A

No, it is defined up to a gradient (as opposed to constant for electro)

39
Q

Derive the magneto equivalent of poisons equation with solution

A
40
Q

Deduce vector potential for B produced by an infinitely long wire carrying charge I = Iez and coinciding with z

A
41
Q

Derive the first 2 terms of multiple expansion for magnetic field

A