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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. Center of Mass: Kinetic Energy & Angular Momentum
KE = 1/2 * µ (dr/dt)² L = µ r x v
<T> = -<V>/2
?? = h/mc * (1-cos(?))
Z²/n² (m_red/m_elec)

2. Atom: Positronium Reduced Mass
?mv
?_max = b/T
µ = m_e/2
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

3. De Broigle Wavelength
Dp/dt = L / (t ?V)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
(3/2) n R ?t
? = h/mv

4. Compton Scattering
µ0 I / 2pR
U - ts = -tlog(Z)
Cos[?] Sin[?] -Sin[?] Cos[?]
?? = h/mc * (1-cos(?))

5. Magnetic Dipole Moment and Torque
I = -(c ?t)^2 + d^2
F = R/2
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
µ = Current * Area T = µ x B

6. Quant: Orthogonality of States
P/A = s T^4
<?1|?2> = 0 ? Orthogonal
(° of Freedom)kT/2
E = <?| H |?>

7. Bohr Model: Radii
P1V1 - P2V2 / (? - 1)
N²/Z (m_elec/m_red)
?max = 2.898 x 10 -³ / T
Measurements close to true value

8. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
Const: 2t = (n +.5)? Destructive 2t = n?
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
?mv

9. Bragg'S Law of Reflection
? = h/mv
M? = 2dsin(?)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
DW = P dV

10. EM: Maxwell'S equations
<?|O|?>
?mv
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 = T - V dL/dq = d/dt dL/dqdot

11. Magnetic field due to a segment of wire
? exp(-e/t)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
?_max = b/T
H = H_0 + ?H

12. Stoke'S Theorem
B = µ0 I n
? (t-vx/c²)
I = I_0 Cos[?]^2
Int ( A . dr) = Int ( del x A) dSurface

13. Adiabatic means
µ = Current * Area T = µ x B
Isentropic
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Measurements close to true value

14. Boltzmann / Canonical distribution
X_L = X_C or X_total = 0
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
F = mv²/r
P1V1 - P2V2 / (? - 1)

15. Relativistic Momentum
V(r) + L²2/2mr²
<T> = 1/2 * <dV/dx>
?mv
?~T

16. Relativistic Energy
1/vLC
? = ?0 root((1-v/c)/(1+v/c))
C = 4pe0 ab/(a-b) = inner and outer radii
?mc²

17. Mech: Centripetal Force
?max = 2.898 x 10 -³ / T
Isentropic
F = mv²/r
I_z = I_x + I_y (think hoop symmetry)

18. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
DW = P dV
Z²/n² (m_red/m_elec)
B = µ0 I n

19. Stark Effect
B = µ0 I n
J = ? Fdt
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
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

20. Induced EMF of solenoid
P1V1 - P2V2 / (? - 1)
Isentropic
1/vLC
N d flux / dt

21. Entropy (# of states - and in terms of other thermo quantities)
S = k ln[O] ; dS = dQ/T
? = 5/3
Faraday/Lenz: current inducted opposes the changing field
4H + 2e- ? He +2? + 6?

22. Helmholtz Free Energy
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
U - ts = -tlog(Z)

23. Single Slit Diffraction Intensity
? = h/p
? = 1.22?/D
I = Im (sinc²(a)) ; a = pai sin(?) / ?
? = 5/3

24. Rocket Thrust
u dm/dt
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
B = µ0 I n
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

25. Anomalous Zeeman Effect

26. Commutator identities ( [B -A C] - [A -B] )
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
ds² = (c*dt)² - ?(x_i)²
Z_c = -i/(?C) ; Z_L = i ? L
U - ts = -tlog(Z)

27. Coriolis Force
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Exponentially decreasing radial function
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = -2*m(? x r)

28. Astro: Kepler'S Third Law
<?1|?2> = 0 ? Orthogonal
u dm/dt
U = t^2 d/dt (logZ)
P² ~ R³

29. Internal Energy of an Ideal Gas
C_eq = ?C_i
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
(3/2) n R ?t
N d flux / dt

30. Invariant spatial quantity
P1V1 - P2V2 / (? - 1)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Ct²-x²-y²-z²
E = s/e_0

31. Atom: Orbital Config
? = 1.22? / d
N d flux / dt
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
?~1/T

32. Quant: [L_x -L_y] = ?
I = Im (sinc²(a)) ; a = pai sin(?) / ?
ih_barL_z
µ0 I1I2 / (2pd)
C_eq = (? 1/C_i)^-1

33. Lab: Standard Deviation of Poisson
0
dU = 0 ? dS = ?dW/T
DS = 0 - dQ = 0 - P V^? = constant
v(mean)

34. Perturbations
Z = ?g_i*exp(-E/kT)
?mc²
H = H_0 + ?H
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

35. QM: de Broglie Wavelength
?= h/v(2mE)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
?_max = b/T
M? = 2dsin(?)

36. EM: Method of Images
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Opposing charge induced upon conductor
U = t^2 d/dt (logZ)
ih_barL_z

37. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
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
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
F = µ0 q v I / 2pr

38. Mech: Rotational Energy
E = Z²*E1
P/A = s T^4
T = I?²/2
? = 5/3

39. Energy in Inductor
Cos[?] Sin[?] -Sin[?] Cos[?]
C = 4pe0 ab/(a-b) = inner and outer radii
DW/dq
.5 LI²

40. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
I = I_cm + md²
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Ct²-x²-y²-z²

41. Hamiltonian and Hamilton'S equations
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Measurements close to true value
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
N²/Z (m_elec/m_red)

42. Magnetic Field Through Ring
µ0 I / 2R
dQ = dW +dU
F_f = µ*F_N
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

43. Quant: Commutator Relation [AB -C]
E = Z²*E1
A[B -C] + [A -C]B
M? = 2dsin(?)
<?1|?2> = 0 ? Orthogonal

44. Radiation (Larmor - and another neat fact)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Asin(?) = m?
DS = 0 - dQ = 0 - P V^? = constant

45. Solid: Resistivity of Semi-Conductor
? (t-vx/c²)
V = -L di/dt
?~1/T
.5 CV²

46. Hall Coefficient
F = mv²/r
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
1/ne - where n is charge carrier density
F = R/2

47. Lensmaker Equation - Thin Lens
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Cos[?] Sin[?] -Sin[?] Cos[?]
P/A = s T^4
F = µ0 q v I / 2pr

48. Self Inductance
Z_c = -i/(?C) ; Z_L = i ? L
V = -L di/dt
Asin(?) = m?
C = 4pe0 ab/(a-b) = inner and outer radii

49. Solid: Resistivity of Metal
.5 CV²
?_max = b/T
?~T
Measurements close to mean

50. Thermo: Partition Function
P +1/2 ? v² + ?gh = Constant
?? = h/mc * (1-cos(?))
Z = ?g_i*exp(-E/kT)
?max = 2.898 x 10 -³ / T