Week 6 Flashcards
Magnetic part of Lorentz force law
Magnetism analogue of Coloumb’s law
Which is force on test charge Q, moving with velocity v in magnetic field B
Why are the velocities in magnetostatics?
The movement of charges causes a static magnetic field (unchanging magnetic field)
Right hand rule
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
Lorentz force law
Prove that the force on a closed loop of wire carrying current I due to a constant magnetic field B is zero
The size of force due to a magnetic field is?
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
Interesting consequence of force law
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
Magnetic forces and work
Fmagnetic is perpendicular to v therefore force due to magnetic field does not do any work as
Fmagnetic • dl = Fmagnetic • vdt = 0
Magnetic forces can’t accelerate a charged particle, only alter direction that test charges move
A current is
A charge in motion
Units for current
1 Ampere = 1 coulomb per second
Current vector points
In the direction opposite to the movement of electrons
Calculate Fmagnetic for charge density λ and on a length of wire
Define the magnetic force on a surface
Define a magnetic force through a volume
Derive the continuity equation
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
Steady current
No build up of charge