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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. Single Slit Diffraction Maximum
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.
L = T - V dL/dq = d/dt dL/dqdot
I_z = I_x + I_y (think hoop symmetry)
Asin(?) = m?

2. Malus Law

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3. Gibbs Factor
Exp(N(µ-e)/t)
1/ne - where n is charge carrier density
v(mean)
P/A = s T^4

4. Focal point of mirrror with curvature
F = s * T4
F = R/2
P² ~ R³
? = 5/3

5. Spherical Capacitor Equation
F = µ0 q v I / 2pr
F = I L X B
C = 4pe0 ab/(a-b) = inner and outer radii
Measurements close to mean

6. Bernoulli Equation
P +1/2 ? v² + ?gh = Constant
I = V/R exp(-t/RC)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
F = I L X B

7. Lab: Precision of Measurements
? (t-vx/c²)
Measurements close to mean
F = s * T4
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

8. Doppler Shift in Frequency
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
F = f* (c+v_r)/(c+v_s)
Exp(N(µ-e)/t)

9. First law of thermodynamics (explain direction of energy for each term)
F_f = µ*F_N
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
? = 1.22? / d

10. EM: SHO (Hooke)
Z = ?g_i*exp(-E/kT)
ih_barL_z
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
ma + kx = 0

11. Quant: Eigenvalue of Hermitian Operator
Always Real
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
? = 1.22?/D

12. Stark Effect
.5 LI²
V = -L di/dt
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
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

13. Bar magnets -- direction of B field lines - earth'S B field
NC?T
F = mv²/r
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
?max = 2.898 x 10 -³ / T

14. Adiabatic means
?~1/T
Isentropic
E = Z²*E1
P² ~ R³

15. Radiation (Larmor - and another neat fact)
µ = Current * Area T = µ x B
P1V1 - P2V2 / (? - 1)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

16. Astro: p-p Chain
.5 CV²
DW = P dV
µ0 I / 2pR
4H + 2e- ? He +2? + 6?

17. Law of Mass Action
V = -L di/dt
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
I = -(c ?t)^2 + d^2
µ=s^2

18. Solid: Resistivity of Metal
X_L = X_C or X_total = 0
I = I_cm + (1/2)m d^2
?~T
PdV +dU

19. Magnetic field due to a segment of wire
P/A = s T^4
Infinitely close to equilibrium at all times
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
1/vLC

20. Hamiltonian and Hamilton'S equations
P/A = s T^4
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

21. Entropy (# of states - and in terms of other thermo quantities)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
v(mean)
S = k ln[O] ; dS = dQ/T
Const: 2t = (n +.5)? Destructive 2t = n?

22. EM: Maxwell'S equations
? = 1.22? / d
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
dQ = dW +dU
ih_barL_z

23. Internal Energy of an Ideal Gas
DS = 0 - dQ = 0 - P V^? = constant
(3/2) n R ?t
? = h/p
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

24. Rotation matrix (2x2)
NC?T
Cos[?] Sin[?] -Sin[?] Cos[?]
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
X_C = 1/(i?C)

25. Helmholtz Free Energy
?max = 2.898 x 10 -³ / T
U - ts = -tlog(Z)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

26. Lensmaker Equation - Thin Lens
S = k ln[O] ; dS = dQ/T
? (t-vx/c²)
? = ?0 root((1-v/c)/(1+v/c))
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

27. Effective Potential
V(r) + L²2/2mr²
<T> = 1/2 * <dV/dx>
F = I L X B
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

28. 3 Laws of Thermo
?? = h/mc * (1-cos(?))
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

29. Solid: Resistivity of Semi-Conductor
S_mean = s/Sqrt[N]
?~1/T
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

30. Invariant Energy Quantity
?s = 0 - ?l = ±1
N²/Z (m_elec/m_red)
E²-p²c²
? = h/mv

31. Thermo: Average Total Energy
(° of Freedom)kT/2
? = h/mv
V = V0 + V0 a ?T
KE = 1/2 * µ (dr/dt)² L = µ r x v

32. Mean electron drift speed
?mv
J/(ne) n: atom density
I = -(c ?t)^2 + d^2
S_mean = s/Sqrt[N]

33. Selection Rules
J/(ne) n: atom density
Ct²-x²-y²-z²
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
?s = 0 - ?l = ±1

34. Mech: Centripetal Force
4H + 2e- ? He +2? + 6?
F = mv²/r
1/2 CV²
ma + kx = 0

35. Mech: Force of Friction
Exponentially decreasing radial function
C_eq = ?C_i
u dm/dt
F_f = µ*F_N

36. SR: Spacetime Interval
T = I?²/2
L = T - V dL/dq = d/dt dL/dqdot
ds² = (c*dt)² - ?(x_i)²
KE = 1/2 * µ (dr/dt)² L = µ r x v

37. Angular momentum - Central Force Motion
B = µ0 I n
Infinitely close to equilibrium at all times
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
L = mr²d?/dt

38. Atom: Bohr Formula
E = Z²*E1
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
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
J/(ne) n: atom density

39. Partition Function
Exponentially decreasing radial function
Z = ?g_i*exp(-E/kT)
? exp(-e/t)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

40. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
PdV +dU
T^2 = k R^3 - k=constant
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

41. QM: de Broglie Wavelength
? exp(-e/t)
?= h/v(2mE)
?~T
Infinitely close to equilibrium at all times

42. Thermo: Partition Function
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
µ0 I / 2R
DW/dq
Z = ?g_i*exp(-E/kT)

43. Self Inductance
Cv = dE/dT = 3R
u dm/dt
V = -L di/dt
Q = CVexp(-t/RC)

44. Energy in Inductor
.5 LI²
U - ts = -tlog(Z)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
µ=s^2

45. Thermo: Blackbody Radiation
F = s * T4
Hbar*?³/(p²c³exp(hbar?/t)-1)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

46. Polarizers - intensity when crossed at ?
? exp(-e/t)
Opposing charge induced upon conductor
<T> = -<V>/2
I = I_0 Cos[?]^2

47. Force on a wire in magnetic field
F = I L X B
I = V/R exp(-t/RC)
L = L_0 Sqrt[1-v^2/c^2]
Sin(?) = ?/d

48. Lab: Standard Deviation of Poisson
Faraday/Lenz: current inducted opposes the changing field
Hbar*?³/(p²c³exp(hbar?/t)-1)
? = h/mv
v(mean)

49. Magnetic Field of a long solenoid
Asin(?) = m?
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Z = ?g_i*exp(-E/kT)
B = µ0 I n

50. Atom: Orbital Config
Const: 2t = (n +.5)? Destructive 2t = n?
1/ne - where n is charge carrier density
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave