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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. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
0
T^2 = k R^3 - k=constant

2. Mean electron drift speed
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Z = ?g_i*exp(-E/kT)
X_C = 1/(i?C)
J/(ne) n: atom density

3. Magnetic Dipole Moment and Torque
µ=s^2
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
µ = Current * Area T = µ x B
1/vLC

4. Work in a capacitor
X_L = i?L
1/2 CV²
Measurements close to mean
Cv = dE/dT = 3R

5. Magnetic Field For Current in Long Wire
µ0 I / 2pR
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
L = L_0 Sqrt[1-v^2/c^2]
µ = m_e/2

6. Lab: Standard Deviation of Poisson
?? = h/mc * (1-cos(?))
v(mean)
Ct²-x²-y²-z²
V = V0 + V0 a ?T

7. EM: Reactance of Inductor
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Measurements close to true value
X_L = i?L
E²-p²c²

8. De Broglie wavelength
<T> = -<V>/2
J = ? Fdt
Cv = dE/dT = 3R
? = h/p

9. Angular momentum - Central Force Motion
L = mr²d?/dt
E = <?| H |?>
NC?T
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

10. Error in the mean if each measurement has the same uncertainty s
S_mean = s/Sqrt[N]
P1V1 - P2V2 / (? - 1)
? = ?0 root((1-v/c)/(1+v/c))
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

11. Electromotive Force
Cos[?] Sin[?] -Sin[?] Cos[?]
C_eq = (? 1/C_i)^-1
µ=s^2
DW/dq

12. Rayleigh'S Criterion
Z = ?g_i*exp(-E/kT)
Sin(?) = ?/d
Cv = dE/dT = 3R
KE = 1/2 * µ (dr/dt)² L = µ r x v

13. Boltzmann / Canonical distribution
Const: 2t = (n +.5)? Destructive 2t = n?
I = Im (sinc²(a)) ; a = pai sin(?) / ?
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
U = t^2 d/dt (logZ)

14. Mech: Parallel Axis Theorem (Moment of Inertia)
? exp(-e/t)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
J = E s - s = Conductivity - E = Electric field
I = I_cm + md²

15. Expectation value of the energy of state |?>
ds² = (c*dt)² - ?(x_i)²
E = <?| H |?>
?s = 0 - ?l = ±1
dQ = dW +dU

16. EM: Parallel Capacitance
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
C_eq = ?C_i
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

17. EM: AC Resonance
KE = 1/2 * µ (dr/dt)² L = µ r x v
X_L = X_C or X_total = 0
Z = ?g_i*exp(-E/kT)
1/2 CV²

18. Spherical Capacitor Equation
F = R/2
C = 4pe0 ab/(a-b) = inner and outer radii
dQ = dW +dU
<?1|?2> = 0 ? Orthogonal

19. E field of a capacitor (d->0)
E = s/e_0
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = I_cm + md²
V = V0 + V0 a ?T

20. Bohr Model: Radii
M? = 2dsin(?)
C = 4pe0 ab/(a-b) = inner and outer radii
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
N²/Z (m_elec/m_red)

21. Relativistic Energy
?mc²
Measurements close to true value
L = L_0 Sqrt[1-v^2/c^2]
S = k ln[O] ; dS = dQ/T

22. Atom: Bohr Formula
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
µ0 I1I2 / (2pd)
ih_barL_z
? = 1.22?/D

23. Bragg'S Law of Reflection
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
M? = 2dsin(?)
I = I_cm + md²
U - ts = -tlog(Z)

24. Lab: Accuracy of Measurements
Measurements close to true value
A[B -C] + [A -C]B
? exp(-e/t)
P1V1 - P2V2 / (? - 1)

25. Invariant spatial quantity
? (t-vx/c²)
Ct²-x²-y²-z²
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
?= h/v(2mE)

26. Energy in terms of partition function
U = t^2 d/dt (logZ)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
? = ?0 root((1-v/c)/(1+v/c))
F = I L X B

27. Doppler Shift in Frequency
?mc²
qvb = mv²/R
F = f* (c+v_r)/(c+v_s)
L = T - V dL/dq = d/dt dL/dqdot

28. Wein'S displacement law for blackbodies (? and T)
?_max = b/T
µ = m_e/2
J = E s - s = Conductivity - E = Electric field
Ct²-x²-y²-z²

29. Rocket Thrust
J = E s - s = Conductivity - E = Electric field
u dm/dt
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
L = L_0 Sqrt[1-v^2/c^2]

30. Quant: Eigenvalue of Hermitian Operator
Cos[?] Sin[?] -Sin[?] Cos[?]
Always Real
Z_c = -i/(?C) ; Z_L = i ? L
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

31. Stefan-Boltzmann law for blackbodies (power per area and T)
<T> = -<V>/2
?mc²
P/A = s T^4
Hbar*?³/(p²c³exp(hbar?/t)-1)

32. Compton Scattering
.5 CV²
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
?? = h/mc * (1-cos(?))
?~T

33. Resistance - length - area - rho
Exp(N(µ-e)/t)
u dm/dt
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

34. 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>
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
F = f* (c+v_r)/(c+v_s)
V = V0 + V0 a ?T

35. Lensmaker Equation - Thin Lens
u dm/dt
F = R/2
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
? (t-vx/c²)

36. Resonance frequency of LC circuit
dU = 0 ? dS = ?dW/T
? = 1.22?/D
1/vLC
µ0 I1I2 / (2pd)

37. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
E = <?| H |?>
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Faraday/Lenz: current inducted opposes the changing field

38. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
I = I_0 Cos[?]^2
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
u dm/dt

39. EM: Method of Images
N²/Z (m_elec/m_red)
P² ~ R³
Opposing charge induced upon conductor
F = I L X B

40. EM: Maxwell'S equations
Exp(N(µ-e)/t)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Opposing charge induced upon conductor
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

41. Atom: Positronium Reduced Mass
µ = m_e/2
B = µ0 I n
T^2 = k R^3 - k=constant
F = -2*m(? x r)

42. Doppler Shift for light
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
<T> = 1/2 * <dV/dx>
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
? = ?0 root((1-v/c)/(1+v/c))

43. Quant: Orthogonality of States
I = I_0 Cos[?]^2
F = qv×B
<?1|?2> = 0 ? Orthogonal
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

44. Dulong Petit Law
I = I_0 Cos[?]^2
Cv = dE/dT = 3R
I ' = I cos²(?)
µ = m_e/2

45. Induced EMF of solenoid
?= h/v(2mE)
N d flux / dt
Isentropic
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

46. How to derive cylcotron frequency
ma + kx = 0
A[B -C] + [A -C]B
?= h/v(2mE)
qvb = mv²/R

47. Inductance of Solenoid
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
I = I_0 Cos[?]^2
Asin(?) = m?

48. Adiabatic processes (dS - dQ - P and V)
DS = 0 - dQ = 0 - P V^? = constant
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Infinitely close to equilibrium at all times
0

49. Hall Coefficient
?mv
1/ne - where n is charge carrier density
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

50. Relativistic Momentum
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Cv = dE/dT = 3R
?mv