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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. SR: Total Energy of a Particle
Asin(?) = m?
E²-p²c²
Sin(?) = ?/d
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

2. Clausius-Clapeyron Equation
? = 1.22? / d
I = I_cm + md²
L = T - V dL/dq = d/dt dL/dqdot
Dp/dt = L / (t ?V)

3. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
.5 LI²
Infinitely close to equilibrium at all times
1/2 CV²

4. EM: Reactance of Capacitor
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
X_C = 1/(i?C)
<?1|?2> = 0 ? Orthogonal
E = <?| H |?>

5. Atom: Positronium Reduced Mass
.5 LI²
<?|O|?>
µ = m_e/2
(° of Freedom)kT/2

6. Angular momentum operators L^2 and L_z
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
(° of Freedom)kT/2
I = I_cm + md²
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

7. Poisson distribution (µ and s)
µ=s^2
Q = CVexp(-t/RC)
?max = 2.898 x 10 -³ / T
DS = 0 - dQ = 0 - P V^? = constant

8. Mech: Force of Friction
J = E s - s = Conductivity - E = Electric field
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
F_f = µ*F_N

9. Work (P - V)
P1V1 - P2V2 / (? - 1)
L = mr²d?/dt
1/2 CV²
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

10. Thermo: Monatomic gas ?=?
? (t-vx/c²)
? = 5/3
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
P +1/2 ? v² + ?gh = Constant

11. Focal point of mirrror with curvature
L = mr²d?/dt
V(r) + L²2/2mr²
Measurements close to mean
F = R/2

12. Bragg'S Law of Reflection
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
M? = 2dsin(?)
µ=s^2
(° of Freedom)kT/2

13. Atom: Bohr Theory Ionization
F = f* (c+v_r)/(c+v_s)
E = Z²*E1
I = I_cm + md²
X_C = 1/(i?C)

14. Invariant spatial quantity
Ct²-x²-y²-z²
Z_c = -i/(?C) ; Z_L = i ? L
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
? = ?0 root((1-v/c)/(1+v/c))

15. Gibbs Factor
T = I?²/2
Exp(N(µ-e)/t)
I = I_0 Cos[?]^2
F_f = µ*F_N

16. Boltzmann / Canonical distribution
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
N d flux / dt
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
4H + 2e- ? He +2? + 6?

17. RLC resonance condition
?= h/v(2mE)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I ' = I cos²(?)
V = -L di/dt

18. Stefan-Boltzmann law for blackbodies (power per area and T)
P/A = s T^4
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
L = L_0 Sqrt[1-v^2/c^2]
Isentropic

19. De Broglie wavelength
? = h/p
DW/dq
I = I_0 Cos[?]^2
Cv = dE/dT = 3R

20. Internal Energy of an Ideal Gas
(3/2) n R ?t
Z = ?g_i*exp(-E/kT)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
1/2 CV²

21. Energy in Inductor
F = f* (c+v_r)/(c+v_s)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
V(r) + L²2/2mr²
.5 LI²

22. EM: Maxwell'S equations
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.
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
? (t-vx/c²)
Isentropic

23. Pauli matrices
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
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
qvb = mv²/R

24. EM: Series Capacitance
E = <?| H |?>
C_eq = (? 1/C_i)^-1
U - ts = -tlog(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

25. Effective Potential
0
V(r) + L²2/2mr²
Cos[?] Sin[?] -Sin[?] Cos[?]
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

26. Solid: Resistivity of Semi-Conductor
T = I?²/2
?~1/T
ma + kx = 0
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

27. SR: Spacetime Interval
Int ( A . dr) = Int ( del x A) dSurface
N d flux / dt
ds² = (c*dt)² - ?(x_i)²
U = t^2 d/dt (logZ)

28. Single Slit Diffraction Maximum
? = h/p
Asin(?) = m?
E = <?| H |?>
(3/2) n R ?t

29. Resonance frequency of LC circuit
(3/2) n R ?t
1/vLC
C_eq = ?C_i
F = -2*m(? x r)

30. Entropy (# of states - and in terms of other thermo quantities)
V = V0 + V0 a ?T
I = Im (sinc²(a)) ; a = pai sin(?) / ?
S = k ln[O] ; dS = dQ/T
E = s/e_0

31. EM: SHO (Hooke)
NC?T
? = 1.22? / d
ma + kx = 0
F = R/2

32. Relativistic Momentum
<?1|?2> = 0 ? Orthogonal
Int ( A . dr) = Int ( del x A) dSurface
?mv
P² ~ R³

33. Addition of relativistic velocities

34. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
dQ = dW +dU
I_z = I_x + I_y (think hoop symmetry)
Ct²-x²-y²-z²

35. Magnetic Dipole Moment and Torque
? = 1.22?/D
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
I_z = I_x + I_y (think hoop symmetry)
µ = Current * Area T = µ x B

36. Stoke'S Theorem
DW/dq
Int ( A . dr) = Int ( del x A) dSurface
.5 LI²
Z = ?g_i*exp(-E/kT)

37. Quant: [L_x -L_y] = ?
Asin(?) = m?
?mc²
ih_barL_z
I = I_cm + (1/2)m d^2

38. Complex impedance (expressions for capacitor and inductor)
Q = CVexp(-t/RC)
X_L = i?L
? exp(-e/t)
Z_c = -i/(?C) ; Z_L = i ? L

39. Angular momentum - Central Force Motion
L = T - V dL/dq = d/dt dL/dqdot
L = mr²d?/dt
F = R/2
?_max = b/T

40. How to derive cylcotron frequency
Z = ?g_i*exp(-E/kT)
qvb = mv²/R
J = ? Fdt
P1V1 - P2V2 / (? - 1)

41. Helmholtz Free Energy
U - ts = -tlog(Z)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
DS = 0 - dQ = 0 - P V^? = constant
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

42. Compton Scattering
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
F = R/2
?max = 2.898 x 10 -³ / T
?? = h/mc * (1-cos(?))

43. Self Inductance
V = -L di/dt
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
E = Z²*E1
? exp(-e/t)

44. Current in resistor in RC circuit
<?|O|?>
X_L = X_C or X_total = 0
E²-p²c²
I = V/R exp(-t/RC)

45. Lensmaker Equation - Thin Lens
1/2 CV²
X_L = X_C or X_total = 0
P/A = s T^4
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

46. Mech: Impulse
N d flux / dt
J = ? Fdt
I = I_cm + (1/2)m d^2
F = qv×B

47. Relativistic Energy
?mc²
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
ih_barL_z
N²/Z (m_elec/m_red)

48. Rocket Thrust
u dm/dt
.5 LI²
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Sin(?) = ?/d

49. Weighted average (mean and unc. of mean)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
?mv
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
E = <?| H |?>

50. EM: Electric Field inside of Conductor
A[B -C] + [A -C]B
0
E = <?| H |?>
Ct²-x²-y²-z²