Chapter 27: Magnetism Flashcards
unit of magnetic field
Tesla, massive amount
why do we have to use f= q (v x B) for magnetic force and not just f = q E like for electirc
no magnetic monopoles, thus saying “q” ina mganetoc sense is not possible
define B (vector) direction
the direction in which the north pole of a compass needle tends to point
restate the concepts encoded in the equation for the magnetic force
F = q(vxB)
F = q (vBsinΘ)
- very much sign dependent, each wuatity sign change will effectively flip the directrion of the force
- force ⟂ B
- force ⟂ velocity of charge
- use RH rule to determine direction of force ( if B not ⟂ to v then you already no that there is not a maximum force),
when does Fb = 0
- q is neutral
- sinΘ = 0,
i.e. Θ = 0 : v //B
Θ= 180 : v // -B
when is Fb at a max
F = q vbsinΘ
sinΘ = 1
when Θ = 90
when do objects experience circular motion
when force is always perpendicular to motion( or its velcoity or force ⟂ velocity , by RH rule)
only if the filed (B in this case) is uniform in time and space. then we know that F is cosntatn but direction is always chanigng,
thus Fb never does any work on the moving charge , F ⟂ motion always , thus cos90 = 0, thsu W = Fdl cos theta= fdl(0) = 0
acceleration in circular motion gievne by
v^2 / R , think of nt coordinateds, centripital acceltration
NII on our Fb in ciruclar motion yields what result for R and the consequences (NB remember, not on formula sheet)
|F| = m |a|
|q| v B = m (v^2/R)
R = mv / |q|B , note here that mv is linear momentum
NII on our Fb in ciruclar motion yields R = mv / qB consequences (NB remember, not on formula sheet)
- if particle has greater initial momentum, i.e. greater mass greater vi, then it will have a larger radius.
- if magnetic field is larger, charge is larger quanity then it will have a smaller radius
what is the expresison for angular speed ω and units
ω = v/ R
unit : radians per second
angualr speed i .t.o q ,B ,m adn the implications
amnimulate NII on the eq of motion for to get
ω = (|q| B) / m
implications
- larger B or q means msmaller radius form radius equation, but it does have a greater ω. this obeys conservation of momentum, has we have smae Pinitial,
- larger m means smaller radius faster speed
- smaller m, larger radius, slower speed
frequency relation to ω and incl T
ω = 2π f, with f = 1/T
T is period pf circular path, time to go round 2π
what motion will we get if V is not perpedicular to B
helical motion, v gets split up into V parrallel and v perpendicular, then v parallel component amounts to 0 and we get result, F = q (v⟂) B , so we are still movign in circular motion but are also moving with the same orginial vi in the forward direction, thsu we geta helical path
Lorentz force
Fnet = F elec + F mag Fnet = qE + q(vxB)
does magnetic force act on stationary objects
no only charges only is they are moving only is B is present hence, F = q(vxB)
results from Oersted Danish scientist
First evidence of relationship between magnetism and moving charge (eletrical
current)
when there is no current, the comapss needle points north ( probs due to earths magnetic currentP)
when there is a current present, then the needle delfects acc the current direction
Magnetic interaction is described in two steps:
- a moving charge generates a magnetic firdl B
2. that magneitc field B exerts a force on any ptoher moving charge present int he field
in a straight current carrying wire, what is the magnitude of the net force due to a magnetic field ⟂ to the direction of the current flow
Fnet = I l B (current x length x magfield)
in a straight current carrying wire, what is the magnitude of the net force due to a magnetic field not always ⟂ to the direction of the current flow
vector :
Fnet = I (LxB)
Fnet = I LBsin Θ
Definition of J , current density, vector J
current per unit charge
J = I/A
J= nqV
change in kinetic energy due to B
0
W=0, by work energy theorem
B ⟂ v always
in a curved current carrying wire, what is the magnitude of the net force due to a magnetic field not always ⟂ to the direction of the current flow
vector eq:
Fnet = ∫ dF = ∫ I (dLXB)
when is the net force due to B zero
in a cicruclar current loop where the B is uniform
B ⟂ v always
Torque eq
vectors: T = r x F = rFsinΘ= (distance from rotaitonal axis to position where force is being applied) x force
what is μ
mu is the magnetic dipole defiend as
μ = I A ( where μ and A are vectors)
RH rule, curl fingers in direction of current and thumb points ot directions of unit vector μ hat
Torque in current carrying loop i.t.o μ
T= μ x B (all vectors)
potential energy i.t.o ϕ in current carrying loop
U(ϕ) = -μ·B = -μBcosϕ with U as a scalar, μ and B as vectors, duh
when is a current carrying loop at a stable equilibirum i.t.o ϕ
when U is at a miniumum (a potential well)
shape of U vs ϕ graph is gpoevrned by eq U(ϕ) = -μBcosϕ .
thus min where cosϕ = -1, i.e where ϕ = 0 (or 360 which is basically 0)
where ϕ = 0
when is a current carrying loop at an unstable equilibirum i.t.o ϕ
- when U is at a maximum ( a potential ‘hill’ of sorts)
- when cosϕ is at 1, U(ϕ) = -μBcosϕ
thus ϕ = 180
when is a current carrying loop at a stable equilibirum NOT i.t.o ϕ but just interms of B and μ directions
a current loop which is free to orientate itself will
minimize its potential energy so that magnetic moment is parallel to the magnetic field.
i.e. ϕ = 0 and cos ϕ = -1 and U( ϕ ) = μB Joules. the potential energy well of the -cosϕ graph
