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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. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
? = h/p
F = I L X B
Dp/dt = L / (t ?V)

2. Lensmaker Equation - Thin Lens
E = <?| H |?>
I = I_cm + (1/2)m d^2
S = k ln[O] ; dS = dQ/T
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

3. Lagrangian and Lagrange'S equation
L = T - V dL/dq = d/dt dL/dqdot
? = 5/3
Braking Radiation
DS = 0 - dQ = 0 - P V^? = constant

4. Self Inductance
V = -L di/dt
J = E s - s = Conductivity - E = Electric field
V = V0 + V0 a ?T
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

5. Relativistic interval (which must remain constant for two events)
P/A = s T^4
Measurements close to mean
Int ( A . dr) = Int ( del x A) dSurface
I = -(c ?t)^2 + d^2

6. Wein'S displacement law for blackbodies (? and T)
µ = m_e/2
E²-p²c²
?_max = b/T
Ct²-x²-y²-z²

7. Kepler'S Three Laws
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
1/vLC
?= h/v(2mE)
L = mr²d?/dt

8. Doppler shift for light
Ct²-x²-y²-z²
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Isentropic
Measurements close to mean

9. Rocket Equation
Dv = -udm/m - v = v0 + u ln(m0/m)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
P² ~ R³
F = R/2

10. Single Slit Diffraction Intensity
F = R/2
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
µ=s^2
I = Im (sinc²(a)) ; a = pai sin(?) / ?

11. Doppler Shift for light
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
? = ?0 root((1-v/c)/(1+v/c))
v(mean)
µ0 I1I2 / (2pd)

12. Time Lorentz Transformation
ih_barL_z
NC?T
? (t-vx/c²)
S = k ln[O] ; dS = dQ/T

13. Mech: Rotational Energy
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = -(c ?t)^2 + d^2
T = I?²/2
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

14. EM: Bremsstrahlung (translation)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Braking Radiation
µ0 I / 2R
L = T - V dL/dq = d/dt dL/dqdot

15. EM: Electric Field inside of Conductor
0
P/A = s T^4
.5 LI²
?~T

16. Perturbations
Cv = dE/dT = 3R
?~T
H = H_0 + ?H
?= h/v(2mE)

17. Force on a wire in magnetic field
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Infinitely close to equilibrium at all times
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
F = I L X B

18. Complex impedance (expressions for capacitor and inductor)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Const: 2t = (n +.5)? Destructive 2t = n?
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Z_c = -i/(?C) ; Z_L = i ? L

19. Mech: Parallel Axis Theorem (Moment of Inertia)
V = V0 + V0 a ?T
I = I_cm + md²
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
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

20. Mech: Centripetal Force
Cv = dE/dT = 3R
DW = P dV
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
F = mv²/r

21. Pauli matrices
J = E s - s = Conductivity - E = Electric field
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
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
?= h/v(2mE)

22. QM: de Broglie Wavelength
? = ?0 root((1-v/c)/(1+v/c))
µ0 I / 2R
I = I_cm + (1/2)m d^2
?= h/v(2mE)

23. Energy in Inductor
.5 LI²
C = 4pe0 ab/(a-b) = inner and outer radii
µ0 I1I2 / (2pd)
Always Real

24. Gibbs Factor
V = V0 + V0 a ?T
?max = 2.898 x 10 -³ / T
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Exp(N(µ-e)/t)

25. Selection Rules
S = k ln[O] ; dS = dQ/T
Z²/n² (m_red/m_elec)
?s = 0 - ?l = ±1
M? = 2dsin(?)

26. Resistance - length - area - rho
L = T - V dL/dq = d/dt dL/dqdot
Faraday/Lenz: current inducted opposes the changing field
<?1|?2> = 0 ? Orthogonal
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

27. Planck Radiation Law
NC?T
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Cos[?] Sin[?] -Sin[?] Cos[?]
Hbar*?³/(p²c³exp(hbar?/t)-1)

28. Double Slit: Interference Minimum - Diffraction Minimum
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
P +1/2 ? v² + ?gh = Constant
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

29. Astro: p-p Chain
<?1|?2> = 0 ? Orthogonal
4H + 2e- ? He +2? + 6?
µ = m_e/2
A[B -C] + [A -C]B

30. Mech: Virial Theorem
<?|O|?>
<T> = 1/2 * <dV/dx>
F = R/2
<T> = -<V>/2

31. Relativistic Energy
A[B -C] + [A -C]B
?mc²
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

32. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
<?1|?2> = 0 ? Orthogonal
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Z_c = -i/(?C) ; Z_L = i ? L
?_max = b/T

33. Inductance of Solenoid
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
µ0 I / 2pR
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
?? = h/mc * (1-cos(?))

34. RLC resonance condition
DW/dq
I_z = I_x + I_y (think hoop symmetry)
µ0 I1I2 / (2pd)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

35. Atom: Orbital Config
I = V/R exp(-t/RC)
? = 5/3
DW = P dV
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

36. Thin Film Theory: Constructive / Destructive Interference
S_mean = s/Sqrt[N]
ds² = (c*dt)² - ?(x_i)²
Const: 2t = (n +.5)? Destructive 2t = n?
?s = 0 - ?l = ±1

37. Magnetic field due to a segment of wire
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
J = E s - s = Conductivity - E = Electric field
?_max = b/T
I = I_0 Cos[?]^2

38. De Broigle Wavelength
µ = Current * Area T = µ x B
Exp(N(µ-e)/t)
? = h/mv
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.

39. Heat added
Dp/dt = L / (t ?V)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
NC?T

40. Stark Effect
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Z_c = -i/(?C) ; Z_L = i ? L
DS = 0 - dQ = 0 - P V^? = constant
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

41. Boltzmann / Canonical distribution
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
W_A < W_I
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
? = ?0 root((1-v/c)/(1+v/c))

42. Stefan-Boltzmann law for blackbodies (power per area and T)
H = H_0 + ?H
P/A = s T^4
DW = P dV
V = V0 + V0 a ?T

43. Magnetic Field Through Ring
? = h/mv
Z_c = -i/(?C) ; Z_L = i ? L
V(r) + L²2/2mr²
µ0 I / 2R

44. Bar magnets -- direction of B field lines - earth'S B field
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
P +1/2 ? v² + ?gh = Constant
? exp(-e/t)
?~T

45. EM: Maxwell'S equations
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Z = ?g_i*exp(-E/kT)
µ0 I1I2 / (2pd)

46. Induced EMF of solenoid
I = I_0 Cos[?]^2
N d flux / dt
Infinitely close to equilibrium at all times
Const: 2t = (n +.5)? Destructive 2t = n?

47. Charge in Capacitor
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
U - ts = -tlog(Z)
Q = CVexp(-t/RC)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

48. Volumetric Expansion
Hbar*?³/(p²c³exp(hbar?/t)-1)
DS = 0 - dQ = 0 - P V^? = constant
V = V0 + V0 a ?T
? = 1.22?/D

49. EM: SHO (Hooke)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?mc²
ma + kx = 0
N d flux / dt

50. Spherical Capacitor Equation
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
C = 4pe0 ab/(a-b) = inner and outer radii
C_eq = ?C_i
F = I L X B