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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. EM: Electromagnetic inertia
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
M? = 2dsin(?)
Faraday/Lenz: current inducted opposes the changing field
DS = 0 - dQ = 0 - P V^? = constant

2. Hamiltonian and Hamilton'S equations
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
E = s/e_0
N d flux / dt

3. Resonance frequency of LC circuit
Z = ?g_i*exp(-E/kT)
1/vLC
Z_c = -i/(?C) ; Z_L = i ? L
Hbar*?³/(p²c³exp(hbar?/t)-1)

4. Thermo: Partition Function
4H + 2e- ? He +2? + 6?
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?mv
Z = ?g_i*exp(-E/kT)

5. Mech: Parallel Axis Theorem (Moment of Inertia)
Sin(?) = ?/d
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
<?1|?2> = 0 ? Orthogonal
I = I_cm + md²

6. Resistance - length - area - rho
I_z = I_x + I_y (think hoop symmetry)
E = Z²*E1
Cos[?] Sin[?] -Sin[?] Cos[?]
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

7. Thermo: Average Total Energy
V = -L di/dt
(° of Freedom)kT/2
Measurements close to mean
U - ts = -tlog(Z)

8. Biot-Savart law
X_L = i?L
M? = 2dsin(?)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
? = 5/3

9. Mech: Rotational Energy
T = I?²/2
E = <?| H |?>
?_max = b/T
.5 LI²

10. Double Slit: Interference Minimum - Diffraction Minimum
J = ? Fdt
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
F = f* (c+v_r)/(c+v_s)
P² ~ R³

11. Atom: Positronium Reduced Mass
KE = 1/2 * µ (dr/dt)² L = µ r x v
F = s * T4
µ = m_e/2
?_max = b/T

12. Entropy (# of states - and in terms of other thermo quantities)
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.
S = k ln[O] ; dS = dQ/T
Const: 2t = (n +.5)? Destructive 2t = n?
M? = 2dsin(?)

13. Relativistic Energy
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Cv = dE/dT = 3R
Exp(N(µ-e)/t)
?mc²

14. Mech: Centripetal Force
? exp(-e/t)
F = mv²/r
µ0 I1I2 / (2pd)
B = µ0 I n

15. Error in the mean if each measurement has the same uncertainty s
P +1/2 ? v² + ?gh = Constant
? = h/mv
S_mean = s/Sqrt[N]
E = s/e_0

16. Mech: Impulse
µ0 I / 2pR
Ct²-x²-y²-z²
J = ? Fdt
Sin(?) = ?/d

17. td(entropy) =
PdV +dU
µ = m_e/2
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
I = I_cm + md²

18. Thermo: 1st Law
.5 CV²
I = I_cm + (1/2)m d^2
v(mean)
dQ = dW +dU

19. Rocket Thrust
u dm/dt
F = s * T4
? = h/p
X_L = X_C or X_total = 0

20. Rayleigh criterion
T = I?²/2
?mv
? = 1.22? / d
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

21. Dulong Petit Law
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
Cv = dE/dT = 3R
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
I = I_cm + md²

22. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
DW/dq
µ = m_e/2

23. Poisson distribution (µ and s)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Dp/dt = L / (t ?V)
F = -2*m(? x r)
µ=s^2

24. Magnetic Field For Current in Long Wire
µ0 I / 2pR
Cv = dE/dT = 3R
v(mean)
.5 CV²

25. EM: Electric Field inside of Conductor
L = T - V dL/dq = d/dt dL/dqdot
I = Im (sinc²(a)) ; a = pai sin(?) / ?
0
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

26. Heat added
NC?T
? = 5/3
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
C_eq = (? 1/C_i)^-1

27. EM: Parallel Capacitance
P +1/2 ? v² + ?gh = Constant
E²-p²c²
C_eq = ?C_i
Asin(?) = m?

28. Single Slit Diffraction Maximum
Asin(?) = m?
?~T
L = L_0 Sqrt[1-v^2/c^2]
Measurements close to mean

29. EM: Bremsstrahlung (translation)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
1/2 CV²
Braking Radiation

30. Work done on a gas
Z_c = -i/(?C) ; Z_L = i ? L
? (t-vx/c²)
.5 LI²
DW = P dV

31. A reversible process stays..
Infinitely close to equilibrium at all times
dQ = dW +dU
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

32. QM: de Broglie Wavelength
V = -L di/dt
X_L = X_C or X_total = 0
Faraday/Lenz: current inducted opposes the changing field
?= h/v(2mE)

33. Doppler Shift in Frequency
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
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)
KE = 1/2 * µ (dr/dt)² L = µ r x v

34. Wein'S displacement law for blackbodies (? and T)
?_max = b/T
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
P +1/2 ? v² + ?gh = Constant
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

35. Quant: Eigenvalue of Hermitian Operator
Always Real
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
A[B -C] + [A -C]B
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

36. Work (P - V)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
P1V1 - P2V2 / (? - 1)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

37. Thermo: Monatomic gas ?=?
? = 5/3
F_f = µ*F_N
? = 1.22? / d
J = E s - s = Conductivity - E = Electric field

38. Atom: Bohr Theory Ionization
E = Z²*E1
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
µ0 I / 2pR
?_max = b/T

39. Center of Mass: Kinetic Energy & Angular Momentum
µ = Current * Area T = µ x B
KE = 1/2 * µ (dr/dt)² L = µ r x v
I = I_0 Cos[?]^2
Const: 2t = (n +.5)? Destructive 2t = n?

40. Bernoulli Equation
S = k ln[O] ; dS = dQ/T
V = -L di/dt
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
P +1/2 ? v² + ?gh = Constant

41. Quant: [L_x -L_y] = ?
?= h/v(2mE)
W_A < W_I
?s = 0 - ?l = ±1
ih_barL_z

42. Rayleigh'S Criterion
Hbar*?³/(p²c³exp(hbar?/t)-1)
Sin(?) = ?/d
A[B -C] + [A -C]B
Exponentially decreasing radial function

43. Partition Function
(3/2) n R ?t
I = I_0 Cos[?]^2
? exp(-e/t)
T = I?²/2

44. Solid: Resistivity of Metal
u dm/dt
F = f* (c+v_r)/(c+v_s)
?~T
µ = Current * Area T = µ x B

45. EM: Method of Images
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
1/vLC
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Opposing charge induced upon conductor

46. Coriolis Force
?mv
F = -2*m(? x r)
J/(ne) n: atom density
P² ~ R³

47. Time Lorentz Transformation
? (t-vx/c²)
µ0 I / 2pR
1/ne - where n is charge carrier density
v(mean)

48. Quant: Expectation Value
Z_c = -i/(?C) ; Z_L = i ? L
<T> = -<V>/2
<?|O|?>
S_mean = s/Sqrt[N]

49. Anomalous Zeeman Effect

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50. SR: Spacetime Interval
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
Z = ?g_i*exp(-E/kT)
dQ = dW +dU
ds² = (c*dt)² - ?(x_i)²