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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. Mech: Rotational Energy
T = I?²/2
V(r) + L²2/2mr²
?mv
dU = 0 ? dS = ?dW/T

2. Mech: Centripetal Force
µ = m_e/2
F = µ0 q v I / 2pr
F = mv²/r
? = 5/3

3. Mech: Parallel Axis Theorem (Moment of Inertia)
I = I_cm + md²
Cos[?] Sin[?] -Sin[?] Cos[?]
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I_z = I_x + I_y (think hoop symmetry)

4. Angular momentum operators L^2 and L_z
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
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.
<?1|?2> = 0 ? Orthogonal
1/ne - where n is charge carrier density

5. Focal point of mirrror with curvature
S = k ln[O] ; dS = dQ/T
F = R/2
U - ts = -tlog(Z)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

6. Quant: Eigenvalue of Hermitian Operator
Always Real
V = -L di/dt
Exp(N(µ-e)/t)
V(r) + L²2/2mr²

7. Perturbations
Hbar*?³/(p²c³exp(hbar?/t)-1)
H = H_0 + ?H
Z = ?g_i*exp(-E/kT)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

8. De Broglie wavelength
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
? = h/p
F_f = µ*F_N
?= h/v(2mE)

9. Thermo: Isothermal
dU = 0 ? dS = ?dW/T
S_mean = s/Sqrt[N]
F_f = µ*F_N
0

10. Doppler shift for light
H = H_0 + ?H
I ' = I cos²(?)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
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

11. EM: Parallel Capacitance
V(r) + L²2/2mr²
C_eq = ?C_i
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
P/A = s T^4

12. Quant: Orthogonality of States
v(mean)
L = L_0 Sqrt[1-v^2/c^2]
<?1|?2> = 0 ? Orthogonal
P² ~ R³

13. Invariant Energy Quantity
E²-p²c²
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
Faraday/Lenz: current inducted opposes the changing field
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

14. Poisson distribution (µ and s)
F = I L X B
µ=s^2
V(r) + L²2/2mr²
? (t-vx/c²)

15. Single Slit Diffraction Intensity
?mc²
?? = h/mc * (1-cos(?))
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

16. Thin Film Theory: Constructive / Destructive Interference
P1V1 - P2V2 / (? - 1)
Const: 2t = (n +.5)? Destructive 2t = n?
Exponentially decreasing radial function
Measurements close to mean

17. EM: Lorentz Force
F = qv×B
F = R/2
ma + kx = 0
E = Z²*E1

18. Bohr Model: Energy
U = t^2 d/dt (logZ)
J/(ne) n: atom density
DW = P dV
Z²/n² (m_red/m_elec)

19. Atom: Bohr Formula
Z²/n² (m_red/m_elec)
Cv = dE/dT = 3R
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

20. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
I = I_cm + md²
C_eq = (? 1/C_i)^-1
ma + kx = 0

21. Effective Potential
L = L_0 Sqrt[1-v^2/c^2]
Exponentially decreasing radial function
V(r) + L²2/2mr²
Int ( A . dr) = Int ( del x A) dSurface

22. Force/length between two wires
µ0 I1I2 / (2pd)
0
I_z = I_x + I_y (think hoop symmetry)
qvb = mv²/R

23. Wein'S displacement law for blackbodies (? and T)
F = mv²/r
C_eq = (? 1/C_i)^-1
?_max = b/T
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

24. Resistance - length - area - rho
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
V = V0 + V0 a ?T
P1V1 - P2V2 / (? - 1)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

25. Gibbs Factor
Exp(N(µ-e)/t)
I ' = I cos²(?)
F = I L X B
E = s/e_0

26. Relativistic Energy
Infinitely close to equilibrium at all times
µ0 I / 2R
?mc²
Asin(?) = m?

27. Bragg'S Law of Reflection
F = mv²/r
F = f* (c+v_r)/(c+v_s)
<T> = -<V>/2
M? = 2dsin(?)

28. Rotation matrix (2x2)
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
Cos[?] Sin[?] -Sin[?] Cos[?]
L = T - V dL/dq = d/dt dL/dqdot
µ0 I1I2 / (2pd)

29. EM: Electromagnetic inertia
Faraday/Lenz: current inducted opposes the changing field
F_f = µ*F_N
X_L = X_C or X_total = 0
Dp/dt = L / (t ?V)

30. Coriolis Force
W_A < W_I
F = -2*m(? x r)
P/A = s T^4
PdV +dU

31. EM: Method of Images
µ = m_e/2
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
µ0 I / 2pR
Opposing charge induced upon conductor

32. Relativistic interval (which must remain constant for two events)
I = -(c ?t)^2 + d^2
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
F = I L X B
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.

33. Selection Rules
?s = 0 - ?l = ±1
?? = h/mc * (1-cos(?))
1/ne - where n is charge carrier density
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

34. De Broigle Wavelength
? = h/mv
?~1/T
I_z = I_x + I_y (think hoop symmetry)
? = 1.22? / d

35. Planck Radiation Law
E = s/e_0
Hbar*?³/(p²c³exp(hbar?/t)-1)
Z²/n² (m_red/m_elec)
M? = 2dsin(?)

36. Bernoulli Equation
P +1/2 ? v² + ?gh = Constant
.5 LI²
Infinitely close to equilibrium at all times
S_mean = s/Sqrt[N]

37. Source Free RL Circuit
DW/dq
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
F_f = µ*F_N
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

38. Source-free RC Circuit
?mc²
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
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

39. Pauli matrices
µ0 I / 2R
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
?= h/v(2mE)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

40. Doppler Shift in Frequency
<T> = -<V>/2
F = f* (c+v_r)/(c+v_s)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Braking Radiation

41. Adiabatic processes (dS - dQ - P and V)
DS = 0 - dQ = 0 - P V^? = constant
qvb = mv²/R
µ0 I / 2pR
?s = 0 - ?l = ±1

42. Kepler'S third law (T and R)
X_L = X_C or X_total = 0
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
U = t^2 d/dt (logZ)
T^2 = k R^3 - k=constant

43. Resonance frequency of LC circuit
Faraday/Lenz: current inducted opposes the changing field
1/vLC
F_f = µ*F_N
? = ?0 root((1-v/c)/(1+v/c))

44. Magnetic Field Through Ring
X_C = 1/(i?C)
µ0 I / 2R
PdV +dU
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

45. Atom: Positronium Reduced Mass
µ = m_e/2
C = 4pe0 ab/(a-b) = inner and outer radii
Const: 2t = (n +.5)? Destructive 2t = n?
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

46. Malus Law

47. Hall Coefficient
F = qv×B
X_L = X_C or X_total = 0
1/ne - where n is charge carrier density
P +1/2 ? v² + ?gh = Constant

48. How to derive cylcotron frequency
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
qvb = mv²/R
U - ts = -tlog(Z)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

49. Quant: Expectation Value
Dp/dt = L / (t ?V)
<?|O|?>
u dm/dt
Cv = dE/dT = 3R

50. Lab: Standard Deviation of Poisson
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
v(mean)
F = f* (c+v_r)/(c+v_s)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°