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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Magnetic Dipole Moment and Torque
µ = Current * Area T = µ x B
? = h/p
I ' = I cos²(?)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

2. Expectation value of the energy of state |?>
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
L = mr²d?/dt
I = -(c ?t)^2 + d^2
E = <?| H |?>

3. Electromotive Force
I ' = I cos²(?)
L = L_0 Sqrt[1-v^2/c^2]
DW/dq
F = f* (c+v_r)/(c+v_s)

4. Mech: Force of Friction
C_eq = (? 1/C_i)^-1
J = E s - s = Conductivity - E = Electric field
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
F_f = µ*F_N

5. Doppler Shift for light
Dv = -udm/m - v = v0 + u ln(m0/m)
? = ?0 root((1-v/c)/(1+v/c))
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

6. Quant: [L_x -L_y] = ?
<T> = 1/2 * <dV/dx>
X_C = 1/(i?C)
Opposing charge induced upon conductor
ih_barL_z

7. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
Measurements close to mean
.5 LI²
Asin(?) = m?

8. EM: Reactance of Capacitor
V = V0 + V0 a ?T
C_eq = ?C_i
X_C = 1/(i?C)
Dv = -udm/m - v = v0 + u ln(m0/m)

9. Center of Mass: Kinetic Energy & Angular Momentum
KE = 1/2 * µ (dr/dt)² L = µ r x v
F = I L X B
C_eq = ?C_i
<T> = -<V>/2

10. Single Slit Diffraction Intensity
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
In Zeeman effect - the contribution of electron spin to total angular momentum means that it isn'T always three lines and they are not always equally spaced.
E = s/e_0
I = Im (sinc²(a)) ; a = pai sin(?) / ?

11. Source Free RL Circuit
I = V/R exp(-t/RC)
J = E s - s = Conductivity - E = Electric field
Z²/n² (m_red/m_elec)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

12. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
<?1|?2> = 0 ? Orthogonal

13. Wein'S Displacement Law
NC?T
I = V/R exp(-t/RC)
S = (hbar/2) s ;with S = S_x xhat + S_y yhat + S_z zhat -s = s_x xhat + s_y yhat + s_z zhat
?max = 2.898 x 10 -³ / T

14. Magnetic Field Through Ring
C_eq = ?C_i
?? = h/mc * (1-cos(?))
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
µ0 I / 2R

15. SR: Spacetime Interval
1/ne - where n is charge carrier density
ds² = (c*dt)² - ?(x_i)²
M? = 2dsin(?)
DS = 0 - dQ = 0 - P V^? = constant

16. Double Slit: Interference Minimum - Diffraction Minimum
Faraday/Lenz: current inducted opposes the changing field
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Opposing charge induced upon conductor
Const: 2t = (n +.5)? Destructive 2t = n?

17. Delta Function Potential - type of WF
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
u dm/dt
T^2 = k R^3 - k=constant
ds² = (c*dt)² - ?(x_i)²

18. Quant: Commutator Relation [AB -C]
Braking Radiation
<T> = 1/2 * <dV/dx>
Dp/dt = L / (t ?V)
A[B -C] + [A -C]B

19. Commutator identities ( [B -A C] - [A -B] )
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
<?1|?2> = 0 ? Orthogonal
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

20. Anomalous Zeeman Effect

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21. Astro: Aperture Formula (Rayleigh Criterion)
µ = m_e/2
? = 1.22?/D
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
?max = 2.898 x 10 -³ / T

22. Selection rules for atomic transitions
Sin(?) = ?/d
Z²/n² (m_red/m_elec)
1/vLC
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

23. Invariant Energy Quantity
A[B -C] + [A -C]B
L = mr²d?/dt
? = ?0 root((1-v/c)/(1+v/c))
E²-p²c²

24. Weighted average (mean and unc. of mean)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

25. EM: Parallel Capacitance
C_eq = ?C_i
NC?T
F = mv²/r
A[B -C] + [A -C]B

26. Stoke'S Theorem
ds² = (c*dt)² - ?(x_i)²
S = (hbar/2) s ;with S = S_x xhat + S_y yhat + S_z zhat -s = s_x xhat + s_y yhat + s_z zhat
I = I_cm + md²
Int ( A . dr) = Int ( del x A) dSurface

27. Energy in Inductor
Measurements close to true value
?= h/v(2mE)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
.5 LI²

28. Stark Effect
When you apply a uniform electric field - it induces a dipole moment and interacts with it - and that effect depends on |mj |. So if j is an integer - splits (asymmetrically) into j+1 levels - and if j is a half integer - splits (asymmetrically) into
I_z = I_x + I_y (think hoop symmetry)
?~1/T
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

29. EM: Electromagnetic inertia
P +1/2 ? v² + ?gh = Constant
F = -2*m(? x r)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Faraday/Lenz: current inducted opposes the changing field

30. Bragg'S Law of Reflection
Dv = -udm/m - v = v0 + u ln(m0/m)
PdV +dU
F = f* (c+v_r)/(c+v_s)
M? = 2dsin(?)

31. Lab: Precision of Measurements
µ = Current * Area T = µ x B
Measurements close to mean
µ0 I / 2pR
V = V0 + V0 a ?T

32. Relativistic interval (which must remain constant for two events)
I = -(c ?t)^2 + d^2
1/ne - where n is charge carrier density
PdV +dU
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

33. Energy in terms of partition function
E = Z²*E1
Isentropic
? (t-vx/c²)
U = t^2 d/dt (logZ)

34. Bar magnets -- direction of B field lines - earth'S B field
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
?= h/v(2mE)
In Zeeman effect - the contribution of electron spin to total angular momentum means that it isn'T always three lines and they are not always equally spaced.
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

35. Induced EMF of solenoid
Z = ?g_i*exp(-E/kT)
Q = CVexp(-t/RC)
S = k ln[O] ; dS = dQ/T
N d flux / dt

36. RLC resonance condition
? (t-vx/c²)
E = Z²*E1
F = mv²/r
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

37. EM: SHO (Hooke)
S_mean = s/Sqrt[N]
DS = 0 - dQ = 0 - P V^? = constant
ma + kx = 0
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

38. EM: Bremsstrahlung (translation)
Braking Radiation
J/(ne) n: atom density
1/vLC
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

39. De Broigle Wavelength
? = h/mv
I = V/R exp(-t/RC)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
µ=s^2

40. EM: Series Capacitance
? = ?0 root((1-v/c)/(1+v/c))
P² ~ R³
C_eq = (? 1/C_i)^-1
S = k ln[O] ; dS = dQ/T

41. Solid: Resistivity of Semi-Conductor
?~1/T
U = t^2 d/dt (logZ)
M? = 2dsin(?)
µ0 I / 2pR

42. Current in resistor in RC circuit
F = R/2
<?|O|?>
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
I = V/R exp(-t/RC)

43. Lagrangian and Lagrange'S equation
Isentropic
F = qv×B
µ0 I / 2R
L = T - V dL/dq = d/dt dL/dqdot

44. Wein'S displacement law for blackbodies (? and T)
Int ( A . dr) = Int ( del x A) dSurface
? = 5/3
?= h/v(2mE)
?_max = b/T

45. Bohr Model: Energy
J = ? Fdt
L = L_0 Sqrt[1-v^2/c^2]
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Z²/n² (m_red/m_elec)

46. Relativistic Momentum
P1V1 - P2V2 / (? - 1)
?mv
ma + kx = 0
µ0 I / 2pR

47. Complex impedance (expressions for capacitor and inductor)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Z_c = -i/(?C) ; Z_L = i ? L
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

48. Internal Energy of an Ideal Gas
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
u dm/dt
(3/2) n R ?t
<T> = 1/2 * <dV/dx>

49. Relativistic Energy
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
?mc²
Z²/n² (m_red/m_elec)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

50. Rocket Equation
Dv = -udm/m - v = v0 + u ln(m0/m)
I ' = I cos²(?)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
T^2 = k R^3 - k=constant