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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. Charge in Capacitor
Q = CVexp(-t/RC)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
J = ? Fdt
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

2. Clausius-Clapeyron Equation
µ0 I1I2 / (2pd)
Dp/dt = L / (t ?V)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
dQ = dW +dU

3. Quant: Commutator Relation [AB -C]
A[B -C] + [A -C]B
.5 CV²
ih_barL_z
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

4. Energy levels from the Coulomb potential
F = f* (c+v_r)/(c+v_s)
dU = 0 ? dS = ?dW/T
Ct²-x²-y²-z²
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

5. Relativistic interval (which must remain constant for two events)
I = -(c ?t)^2 + d^2
Int ( A . dr) = Int ( del x A) dSurface
N d flux / dt
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

6. Angular momentum - Central Force Motion
Measurements close to true value
L = mr²d?/dt
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

7. Lab: Standard Deviation of Poisson
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
v(mean)
L = L_0 Sqrt[1-v^2/c^2]
P1V1 - P2V2 / (? - 1)

8. Resonance frequency of LC circuit
Ct²-x²-y²-z²
C = 4pe0 ab/(a-b) = inner and outer radii
1/vLC
ma + kx = 0

9. Solid: Resistivity of Metal
ma + kx = 0
E = s/e_0
P² ~ R³
?~T

10. Magnetic Field Through Ring
µ0 I / 2R
P1V1 - P2V2 / (? - 1)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
F = qv×B

11. Weighted average (mean and unc. of mean)
W_A < W_I
1/2 CV²
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
?mv

12. Springs in series/parallel
? = h/p
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
H = H_0 + ?H
S_mean = s/Sqrt[N]

13. Double Slit: Interference Minimum - Diffraction Minimum
H = H_0 + ?H
? = 1.22? / d
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
(3/2) n R ?t

14. A reversible process stays..
4H + 2e- ? He +2? + 6?
Infinitely close to equilibrium at all times
Cos[?] Sin[?] -Sin[?] Cos[?]
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

15. Coriolis Force
v(mean)
M? = 2dsin(?)
I = I_0 Cos[?]^2
F = -2*m(? x r)

16. Magnetic field due to a segment of wire
X_L = X_C or X_total = 0
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
E = Z²*E1

17. EM: Electric Field inside of Conductor
0
E = <?| H |?>
4H + 2e- ? He +2? + 6?
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

18. Effective Potential
L = mr²d?/dt
?s = 0 - ?l = ±1
V = -L di/dt
V(r) + L²2/2mr²

19. Force/length between two wires
? = h/mv
L = T - V dL/dq = d/dt dL/dqdot
µ0 I1I2 / (2pd)
? = 1.22?/D

20. Force exerted on charge by long wire
L = L_0 Sqrt[1-v^2/c^2]
F = µ0 q v I / 2pr
B = µ0 I n
T^2 = k R^3 - k=constant

21. Mech: Force of Friction
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
F_f = µ*F_N
E = s/e_0
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

22. Rocket Thrust
? = 1.22?/D
S = k ln[O] ; dS = dQ/T
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
u dm/dt

23. Lensmaker Equation - Thin Lens
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
<?|O|?>
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

24. Inductance of Solenoid
C = 4pe0 ab/(a-b) = inner and outer radii
KE = 1/2 * µ (dr/dt)² L = µ r x v
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

25. EM: Reactance of Inductor
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
X_L = i?L
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

26. QM: de Broglie Wavelength
J/(ne) n: atom density
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
1/ne - where n is charge carrier density
?= h/v(2mE)

27. Pauli matrices
<?1|?2> = 0 ? Orthogonal
T^2 = k R^3 - k=constant
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
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

28. Thermo: Partition Function
T = I?²/2
S_mean = s/Sqrt[N]
Z = ?g_i*exp(-E/kT)
Z_c = -i/(?C) ; Z_L = i ? L

29. Astro: Kepler'S Third Law
P² ~ R³
? = 5/3
Hbar*?³/(p²c³exp(hbar?/t)-1)
S = k ln[O] ; dS = dQ/T

30. Rayleigh criterion
?= h/v(2mE)
F = f* (c+v_r)/(c+v_s)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
? = 1.22? / d

31. Planck Radiation Law
J = E s - s = Conductivity - E = Electric field
?? = h/mc * (1-cos(?))
KE = 1/2 * µ (dr/dt)² L = µ r x v
Hbar*?³/(p²c³exp(hbar?/t)-1)

32. Boltzmann / Canonical distribution
Q = CVexp(-t/RC)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Faraday/Lenz: current inducted opposes the changing field
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

33. Parallel axis theorem
I = I_cm + (1/2)m d^2
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
X_L = X_C or X_total = 0

34. How to derive cylcotron frequency
qvb = mv²/R
?= h/v(2mE)
V = -L di/dt
F = qv×B

35. Resistance - length - area - rho
Cv = dE/dT = 3R
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
dQ = dW +dU
B = µ0 I n

36. Relativistic length contraction
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Ct²-x²-y²-z²
L = L_0 Sqrt[1-v^2/c^2]

37. Force on a wire in magnetic field
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
F = I L X B
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.
Int ( A . dr) = Int ( del x A) dSurface

38. Work in a capacitor
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
1/2 CV²
E = <?| H |?>
M? = 2dsin(?)

39. Atom: Bohr Formula
Z = ?g_i*exp(-E/kT)
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
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
X_C = 1/(i?C)

40. Delta Function Potential - type of WF
Z²/n² (m_red/m_elec)
I = I_cm + md²
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
X_L = i?L

41. EM: Parallel Capacitance
?_max = b/T
C_eq = ?C_i
Hbar*?³/(p²c³exp(hbar?/t)-1)
DW/dq

42. Compton Scattering
?? = h/mc * (1-cos(?))
µ=s^2
M? = 2dsin(?)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

43. Quant: Expectation Value
E²-p²c²
Z²/n² (m_red/m_elec)
X_L = i?L
<?|O|?>

44. Poisson distribution (µ and s)
µ=s^2
dQ = dW +dU
Cos[?] Sin[?] -Sin[?] Cos[?]
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.

45. Mech: Virial Theorem
X_L = X_C or X_total = 0
F = qv×B
<T> = -<V>/2
qvb = mv²/R

46. Invariant spatial quantity
0
Dv = -udm/m - v = v0 + u ln(m0/m)
? (t-vx/c²)
Ct²-x²-y²-z²

47. Bohr Model: Energy
F = s * T4
Z²/n² (m_red/m_elec)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Int ( A . dr) = Int ( del x A) dSurface

48. Energy in Inductor
.5 LI²
I ' = I cos²(?)
µ = Current * Area T = µ x B
?~1/T

49. Hamiltonian and Hamilton'S equations
DW/dq
V = V0 + V0 a ?T
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

50. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
?s = 0 - ?l = ±1
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
<?|O|?>