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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. Angular momentum operators L^2 and L_z
I ' = I cos²(?)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
I = V/R exp(-t/RC)
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

2. Force/length between two wires
F = s * T4
W_A < W_I
µ0 I1I2 / (2pd)
E²-p²c²

3. Thermo: Blackbody Radiation
F = s * T4
Exponentially decreasing radial function
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
?mc²

4. Resistance - length - area - rho
P² ~ R³
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
?? = h/mc * (1-cos(?))

5. Quant: Eigenvalue of Hermitian Operator
F = -2*m(? x r)
Always Real
?= h/v(2mE)
µ = m_e/2

6. Astro: Aperture Formula (Rayleigh Criterion)
?~1/T
(3/2) n R ?t
? = 1.22?/D
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

7. Dulong Petit Law
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.
Cv = dE/dT = 3R
Opposing charge induced upon conductor
<?|O|?>

8. Work in a capacitor
1/2 CV²
S = k ln[O] ; dS = dQ/T
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
W' = (w-v)/(1-w v/c^2) ; observer in S sees an object moving at velocity w; another frame S' moves at v wrt S.

9. Induced EMF of solenoid
<T> = -<V>/2
N d flux / dt
? = 5/3
ih_barL_z

10. Mech: Virial Theorem
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
<T> = -<V>/2
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
4H + 2e- ? He +2? + 6?

11. Heat added
NC?T
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
<T> = 1/2 * <dV/dx>
T^2 = k R^3 - k=constant

12. Magnetic Field of a long solenoid
Const: 2t = (n +.5)? Destructive 2t = n?
(3/2) n R ?t
ds² = (c*dt)² - ?(x_i)²
B = µ0 I n

13. Mech: Rotational Energy
I ' = I cos²(?)
(3/2) n R ?t
T = I?²/2
v(mean)

14. Resonance frequency of LC circuit
1/vLC
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
L = T - V dL/dq = d/dt dL/dqdot
? = 5/3

15. Energy in terms of partition function
DW/dq
T^2 = k R^3 - k=constant
U = t^2 d/dt (logZ)
Dv = -udm/m - v = v0 + u ln(m0/m)

16. Thin Film Theory: Constructive / Destructive Interference
u dm/dt
Const: 2t = (n +.5)? Destructive 2t = n?
?~T
E = Z²*E1

17. Entropy (# of states - and in terms of other thermo quantities)
P/A = s T^4
I = I_cm + (1/2)m d^2
S = k ln[O] ; dS = dQ/T
1/vLC

18. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
Always Real
?s = 0 - ?l = ±1
S = k ln[O] ; dS = dQ/T

19. Springs in series/parallel
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
?= h/v(2mE)
µ0 I / 2R
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

20. Bohr Model: Energy
Int ( A . dr) = Int ( del x A) dSurface
? exp(-e/t)
Measurements close to true value
Z²/n² (m_red/m_elec)

21. Relativistic Energy
?mc²
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Z = ?g_i*exp(-E/kT)

22. Angular momentum - Central Force Motion
S = k ln[O] ; dS = dQ/T
L = mr²d?/dt
P1V1 - P2V2 / (? - 1)
A[B -C] + [A -C]B

23. Inductance of Solenoid
F_f = µ*F_N
I = I_cm + md²
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

24. Quant: Commutator Relation [AB -C]
E = s/e_0
A[B -C] + [A -C]B
L = L_0 Sqrt[1-v^2/c^2]
F = f* (c+v_r)/(c+v_s)

25. Polarizers - intensity when crossed at ?
T^2 = k R^3 - k=constant
I = I_0 Cos[?]^2
F = f* (c+v_r)/(c+v_s)
I ' = I cos²(?)

26. Rotation matrix (2x2)
Faraday/Lenz: current inducted opposes the changing field
I = I_cm + (1/2)m d^2
Cos[?] Sin[?] -Sin[?] Cos[?]
ds² = (c*dt)² - ?(x_i)²

27. Magnetic Dipole Moment and Torque
.5 CV²
µ = Current * Area T = µ x B
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Braking Radiation

28. Lab: Accuracy of Measurements
S = k ln[O] ; dS = dQ/T
Measurements close to true value
.5 CV²
N²/Z (m_elec/m_red)

29. Solid: Resistivity of Metal
F = R/2
?~T
dQ = dW +dU
v(mean)

30. Wein'S Displacement Law
?~T
Infinitely close to equilibrium at all times
? exp(-e/t)
?max = 2.898 x 10 -³ / T

31. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
Int ( A . dr) = Int ( del x A) dSurface
X_L = X_C or X_total = 0
I = -(c ?t)^2 + d^2

32. Current in resistor in RC circuit
I = V/R exp(-t/RC)
µ0 I1I2 / (2pd)
µ=s^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

33. Atom: Positronium Reduced Mass
?s = 0 - ?l = ±1
µ = m_e/2
µ = Current * Area T = µ x B
J = ? Fdt

34. Energy in Inductor
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
C_eq = ?C_i
.5 LI²
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

35. First law of thermodynamics (explain direction of energy for each term)
µ0 I / 2pR
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

36. Charge in Capacitor
Q = CVexp(-t/RC)
?mv
N d flux / dt
<?1|?2> = 0 ? Orthogonal

37. SR: Spacetime Interval
L = mr²d?/dt
F = µ0 q v I / 2pr
ds² = (c*dt)² - ?(x_i)²
U - ts = -tlog(Z)

38. Expectation value of the energy of state |?>
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
DW = P dV
E = <?| H |?>
qvb = mv²/R

39. Hamiltonian and Hamilton'S equations
Exponentially decreasing radial function
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Measurements close to true value
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

40. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
0
E = Z²*E1
T^2 = k R^3 - k=constant

41. EM: Parallel Capacitance
Q = CVexp(-t/RC)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
C_eq = ?C_i
C = 4pe0 ab/(a-b) = inner and outer radii

42. Mech: Impulse
U - ts = -tlog(Z)
J = ? Fdt
Measurements close to true value
µ0 I1I2 / (2pd)

43. EM: Reactance of Inductor
X_L = i?L
? exp(-e/t)
S = k ln[O] ; dS = dQ/T
ds² = (c*dt)² - ?(x_i)²

44. Mean electron drift speed
? exp(-e/t)
4H + 2e- ? He +2? + 6?
J/(ne) n: atom density
X_L = X_C or X_total = 0

45. Rocket Equation
E = s/e_0
Measurements close to true value
Dv = -udm/m - v = v0 + u ln(m0/m)
.5 CV²

46. Atom: Bohr Formula
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Z = ?g_i*exp(-E/kT)
? = 1.22? / d
µ = m_e/2

47. RLC resonance condition
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
T^2 = k R^3 - k=constant

48. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
V(r) + L²2/2mr²
4H + 2e- ? He +2? + 6?

49. Magnetic Field Through Ring
I = I_cm + md²
µ0 I / 2R
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
N d flux / dt

50. Rayleigh'S Criterion
Sin(?) = ?/d
B = µ0 I n
Faraday/Lenz: current inducted opposes the changing field
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)