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64 Cards in this Set
- Front
- Back
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Magnetic field, definition |
B = F_b / |q| v
v = velocity of particle |
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Magnetic force |
F_b = B |q| v |
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EM Equilibrium |
--> forces are balanced
eE = evB
e = elementary charge |
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Potential |
V = v B d |
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Cancelling forces (magnetic and electric) |
B and E must be parallel for their forces to cancel |
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V_d (drift velocity) |
V_d = i / n e A
for an electron |
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When v is perpindicular to the magnetic field, |
The particle will travel in a circular path. |q|vB becomes mv²/r
If there is a || component of v, it moves in a helical path about B |
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Biot Savart Law |
dB = µ₀ / 4π * ( i · ds × r hat) / r² r = distance
Integrate both sides to use |
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Permeability constant |
µ₀ = 1.26 E -6 T · m / Amp = W m |
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B at center of a full circle |
B = µ₀ i / 2 R |
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B on long straight wire |
B = µ₀ i / 2π R
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B at center of circular arc |
B = µ₀ i θ / 4 πR
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What is the orientation of the B vector to the B field lines? (Recall: E is perpendicular to E field lines) |
Tangent to the field lines |
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Density of B field lines is proportional to |
B's magnitude |
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Duality of poles means |
north and south poles can only exist together in pairs (that we know) |
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North and south poles both start & end on |
a pole |
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The magnetic force is maximized when |
velocity of charge is perpendicular to B field |
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The Lorentz force statement states: |
F = qE + q(v × B)
A particle experiences a force with the magnitude equal to the vector addition of the electric force and the magnetic force, when both are present. |
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Use dimensional analysis to determine the equivalent of a Tesla |
(N / Amp meter) |
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What are the two ways to induce a magnetic field? |
1. Using moving electrically charged particles ( electro magnet )
2. Elementary particles, for they have intrinsic magnetic fields. Different arrangement of electrons (diff. materials) yield different magnetic fields. |
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Describe the Hall effect, empirically and in words. |
Electron in uniform electric and magnetic fields does not experience a deflection in its motion. E field must be perpendicular to B field.
F_e = F_b n = Bi / v L e (L = thickness of strip) V drop = vBd |
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Spacing of the magnetic field lines represents |
Decrease in B by a factor of 1/R |
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Ampere's Law |
∫ B · ds = µ₀ i_enc
- evaluated around a closed loop - Uses symmetry like Gauss' law to simplify a situation - i_enclosed = net current
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How to determine direction (Ampere's law) |
Fingers point and curl in direction of integration. current in direction of thumb (+), current opposing (-) |
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When inside the wire, |
B = ( µ₀i / 2 π R² ) · r
r = loop r R = wire R |
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B of ideal solenoid |
B = µ₀∗ i∗ n
n = number of turns per unit length |
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B (inside toroid) |
B =( µ₀ ∗ N ∗ i / 2π ) ∗ 1 / r
r = distance from center to point of interest |
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What is a solenoid? |
Current in a tightly wound helical wire used to induce magnetic field |
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What is a toroid? |
Hollow, curved solenoid. Edges curve until two ends meet, like a bracelet. |
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What is the equation for the magnetic field when the coil acts as a dipole? |
B (z) = (µ₀ / 2π) ∗ ( µ / z³ )
µ = dipole moment z = distance of point P along central axis |
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What is the direction of the µ vector in a dipole coil setting? |
Either in the direction of B or in the opposite (180°) direction of B |
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dF (Differential magnetic force) |
= dq ( v × B ) = i ( dl × B )
F = I L B sin θ |
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Describe the E field and force vectors during Hall effect. |
Field goes from high to low potential; Force points opposite to field |
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What is the motion of a proton's motion in a cyclotron? |
The proton’s speed increases in the gap but not in the circular dee |
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What is the net force on a magnetic dipole? |
0 |
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What does the outstretched thumb represent in the RHR for a current loop in an uniform magnetic field? |
The net torque vector |
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When the magnetic field is along a central axis of a loop |
we find B by summing the parallel components of the field |
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Self induced EMF direction: |
opposes current to oppose the change |
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RL circuits |
Exponentially reach a steady state where they act as a regular wire |
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Torque is |
µ × B |
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Work (in terms of torque) |
∫ T dθ |
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Dipole moment µ |
N i A A = area = a * b |
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Change in potential energy |
∆UE = - N i A B (cos θ_f - cos θ_i) |
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Faraday's Law |
Emf = - dδ / dt ( * N for N amount of turns)
induced by the magnetic flux changing over time |
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Magnetic flux |
δ = ∫ B · dA /// in units of Webers
BA if uniform |
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Lenz's law |
Induced EMF produces a current in direction to oppose the change in flux |
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Electric Equilibrium |
F_e = F_b eE = evB ∴ vB = E |
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Motional EMF |
EMF = v L B L = length |
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Flux |
phi = NBA |
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Energy stored in an inductor |
U = 1/2 L I ² |
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Rate of work (done by you to move loop through magnetic field) |
P = F_b * v = B²L²v²/ R
v= velocity same for thermal energy rate |
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εmf is related to E field by |
ε = ∫ E · ds |
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how is E field related to changing B field? |
∫ E · ds = - dδ / dt
(Faradays law) |
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Work done in one revolution by induced electric field |
W = εmf* q₀ |
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Inductance |
L= N * δ / i |
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Inductance per unit length, solenoid |
= µ₀n²A |
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Self induced εmf |
= - L di / dt |
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Self induced emf (direction) |
opposes change in i |
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Time constant for charge / discharge (capacitor) |
tau = RC |
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Time constant for charge / discharge (inductor) |
tau = L / R |
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Turn on equation of a current, inductor |
i = εmf / R ( 1 - e ^ (- t / tau_L)) |
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Decay of current |
i = i₀ e ^ (-t/tau_L) |
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Magnetic energy |
1/2 L i² (for E, q² / 2C ) |
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Magnetic energy density |
energy density = B² / 2µ₀ |
