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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. Stoke'S Theorem
Exp(N(µ-e)/t)
Int ( A . dr) = Int ( del x A) dSurface
ih_barL_z
I = I_cm + (1/2)m d^2

2. Rocket Thrust
L = mr²d?/dt
Z_c = -i/(?C) ; Z_L = i ? L
u dm/dt
.5 CV²

3. Atom: Hydrogen Wave Function Type
<T> = 1/2 * <dV/dx>
I = I_0 Cos[?]^2
Exponentially decreasing radial function
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

4. Kepler'S third law (T and R)
?? = h/mc * (1-cos(?))
T^2 = k R^3 - k=constant
Measurements close to true value
Ct²-x²-y²-z²

5. Perpendicular axis theorem
I_z = I_x + I_y (think hoop symmetry)
F = R/2
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

6. Quant: Commutator Relation [AB -C]
S = k ln[O] ; dS = dQ/T
A[B -C] + [A -C]B
PdV +dU
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

7. Stark Effect
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.
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
?_max = b/T
T = I?²/2

8. Thermo: Blackbody Radiation
(° of Freedom)kT/2
H = H_0 + ?H
F = s * T4
?mv

9. Selection rules for atomic transitions
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Opposing charge induced upon conductor
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

10. Clausius-Clapeyron Equation
I = V/R exp(-t/RC)
P/A = s T^4
T = I?²/2
Dp/dt = L / (t ?V)

11. Source Free RL Circuit
ds² = (c*dt)² - ?(x_i)²
?s = 0 - ?l = ±1
X_L = X_C or X_total = 0
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

12. Adiabatic processes (dS - dQ - P and V)
E = s/e_0
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.
DS = 0 - dQ = 0 - P V^? = constant
<?1|?2> = 0 ? Orthogonal

13. Induced EMF of solenoid
P +1/2 ? v² + ?gh = Constant
J = ? Fdt
?mv
N d flux / dt

14. Magnetic Dipole Moment and Torque
(3/2) n R ?t
µ = Current * Area T = µ x B
µ = m_e/2
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

15. EM: Electric Field inside of Conductor
L = T - V dL/dq = d/dt dL/dqdot
ma + kx = 0
Cos[?] Sin[?] -Sin[?] Cos[?]
0

16. Dulong Petit Law
X_C = 1/(i?C)
<T> = -<V>/2
Cv = dE/dT = 3R
Z_c = -i/(?C) ; Z_L = i ? L

17. Work done on a gas
<?1|?2> = 0 ? Orthogonal
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Q = CVexp(-t/RC)
DW = P dV

18. Single Slit Diffraction Intensity
NC?T
U = t^2 d/dt (logZ)
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Cv = dE/dT = 3R

19. Thermo: Isothermal
dQ = dW +dU
X_C = 1/(i?C)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
dU = 0 ? dS = ?dW/T

20. Relativistic Energy
Z_c = -i/(?C) ; Z_L = i ? L
F = qv×B
?mc²
µ=s^2

21. Volumetric Expansion
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
V = V0 + V0 a ?T
U - ts = -tlog(Z)
? = ?0 root((1-v/c)/(1+v/c))

22. Parallel axis theorem
Measurements close to true value
I = I_cm + (1/2)m d^2
? = 1.22? / d
T = I?²/2

23. Compton Scattering
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
?? = h/mc * (1-cos(?))
Q = CVexp(-t/RC)
H = H_0 + ?H

24. Biot-Savart law
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
F_f = µ*F_N

25. Coriolis Force
F = -2*m(? x r)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
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.

26. Commutator identities ( [B -A C] - [A -B] )
(3/2) n R ?t
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
N²/Z (m_elec/m_red)
1/ne - where n is charge carrier density

27. Triplet/singlet states: symmetry and net spin
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
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Exp(N(µ-e)/t)

28. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = I_0 Cos[?]^2
Dv = -udm/m - v = v0 + u ln(m0/m)
F = µ0 q v I / 2pr

29. td(entropy) =
Dp/dt = L / (t ?V)
I = I_cm + (1/2)m d^2
PdV +dU
A[B -C] + [A -C]B

30. Resistance - length - area - rho
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Faraday/Lenz: current inducted opposes the changing field
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

31. Quant: Expectation Value
<?|O|?>
Exponentially decreasing radial function
?mv
µ0 I1I2 / (2pd)

32. Thermo: Partition Function
C = 4pe0 ab/(a-b) = inner and outer radii
P² ~ R³
Z = ?g_i*exp(-E/kT)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

33. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
F = s * T4
C = 4pe0 ab/(a-b) = inner and outer radii
1/vLC

34. Time Lorentz Transformation
Opposing charge induced upon conductor
? (t-vx/c²)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
I ' = I cos²(?)

35. Magnetic Field Through Ring
µ0 I / 2R
NC?T
C_eq = (? 1/C_i)^-1
I = I_cm + md²

36. Gibbs Factor
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
F = f* (c+v_r)/(c+v_s)
U - ts = -tlog(Z)
Exp(N(µ-e)/t)

37. Thin Film Theory: Constructive / Destructive Interference
ma + kx = 0
dQ = dW +dU
.5 CV²
Const: 2t = (n +.5)? Destructive 2t = n?

38. Heat added
NC?T
?? = h/mc * (1-cos(?))
?s = 0 - ?l = ±1
0

39. Quant: [L_x -L_y] = ?
F = -2*m(? x r)
ih_barL_z
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
E²-p²c²

40. Magnetic Field For Current in Long Wire
DW/dq
µ0 I / 2pR
I = I_0 Cos[?]^2
P1V1 - P2V2 / (? - 1)

41. Resonance frequency of LC circuit
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
E = <?| H |?>
1/vLC
(° of Freedom)kT/2

42. Current in resistor in RC circuit
I = V/R exp(-t/RC)
F = qv×B
? = h/mv
C_eq = ?C_i

43. EM: Bremsstrahlung (translation)
N d flux / dt
Opposing charge induced upon conductor
Braking Radiation
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.

44. Perturbations
V = V0 + V0 a ?T
H = H_0 + ?H
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
I = I_0 Cos[?]^2

45. Solid: Resistivity of Semi-Conductor
P/A = s T^4
<?|O|?>
?_max = b/T
?~1/T

46. Electromotive Force
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
I = Im (sinc²(a)) ; a = pai sin(?) / ?
DW/dq
E = <?| H |?>

47. EM: Reactance of Inductor
1/ne - where n is charge carrier density
? = 5/3
X_L = i?L
F = I L X B

48. 3 Laws of Thermo
Measurements close to true value
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Cv = dE/dT = 3R
Int ( A . dr) = Int ( del x A) dSurface

49. Hall Coefficient
F_f = µ*F_N
I ' = I cos²(?)
B = µ0 I n
1/ne - where n is charge carrier density

50. EM: SHO (Hooke)
S_mean = s/Sqrt[N]
Sin(?) = ?/d
ma + kx = 0
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration