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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 for light
Cos[?] Sin[?] -Sin[?] Cos[?]
µ0 I / 2pR
?= h/v(2mE)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

2. RLC resonance condition
I_z = I_x + I_y (think hoop symmetry)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
u dm/dt
Q = CVexp(-t/RC)

3. Solid: Resistivity of Metal
M? = 2dsin(?)
Measurements close to mean
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
?~T

4. Relativistic Momentum
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
M? = 2dsin(?)
<?1|?2> = 0 ? Orthogonal
?mv

5. Thermo: Isothermal
X_C = 1/(i?C)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
dU = 0 ? dS = ?dW/T
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

6. Bragg'S Law of Reflection
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
U - ts = -tlog(Z)
qvb = mv²/R
M? = 2dsin(?)

7. De Broigle Wavelength
? = h/mv
P +1/2 ? v² + ?gh = Constant
? = 1.22?/D
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

8. Atom: Bohr Formula
Sin(?) = ?/d
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

9. EM: Electromagnetic inertia
PdV +dU
NC?T
Faraday/Lenz: current inducted opposes the changing field
<T> = 1/2 * <dV/dx>

10. Complex impedance (expressions for capacitor and inductor)
S_mean = s/Sqrt[N]
? = 1.22?/D
Dp/dt = L / (t ?V)
Z_c = -i/(?C) ; Z_L = i ? L

11. Quant: Orthogonality of States
? = ?0 root((1-v/c)/(1+v/c))
?? = h/mc * (1-cos(?))
<?1|?2> = 0 ? Orthogonal
(° of Freedom)kT/2

12. EM: SHO (Hooke)
µ=s^2
C_eq = (? 1/C_i)^-1
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
ma + kx = 0

13. Gibbs Factor
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Exp(N(µ-e)/t)

14. EM: Lorentz Force
F = qv×B
Faraday/Lenz: current inducted opposes the changing field
F = f* (c+v_r)/(c+v_s)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

15. Single Slit Diffraction Intensity
Cv = dE/dT = 3R
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.
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
I = Im (sinc²(a)) ; a = pai sin(?) / ?

16. Thermo: 1st Law
V = V0 + V0 a ?T
B = µ0 I n
dQ = dW +dU
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

17. Thermo: Adiabatic Work vs Isothermal Work
T^2 = k R^3 - k=constant
F = R/2
W_A < W_I
X_L = i?L

18. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
<?|O|?>
.5 CV²
dU = 0 ? dS = ?dW/T

19. Center of Mass: Kinetic Energy & Angular Momentum
KE = 1/2 * µ (dr/dt)² L = µ r x v
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
dU = 0 ? dS = ?dW/T
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

20. Self Inductance
?max = 2.898 x 10 -³ / T
E = s/e_0
P +1/2 ? v² + ?gh = Constant
V = -L di/dt

21. Thermo: Average Total Energy
T^2 = k R^3 - k=constant
I = I_0 Cos[?]^2
(° of Freedom)kT/2
P² ~ R³

22. Biot-Savart law
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
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.
Exp(N(µ-e)/t)
S_mean = s/Sqrt[N]

23. Induced EMF of solenoid
PdV +dU
Int ( A . dr) = Int ( del x A) dSurface
N d flux / dt
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

24. Force on a wire in magnetic field
J = E s - s = Conductivity - E = Electric field
F = I L X B
Z²/n² (m_red/m_elec)
U - ts = -tlog(Z)

25. Force/length between two wires
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.
T^2 = k R^3 - k=constant
µ0 I1I2 / (2pd)
I = I_cm + (1/2)m d^2

26. Bohr Model: Energy
Dp/dt = L / (t ?V)
Z²/n² (m_red/m_elec)
C_eq = (? 1/C_i)^-1
N d flux / dt

27. Astro: Aperture Formula (Rayleigh Criterion)
V = -L di/dt
ds² = (c*dt)² - ?(x_i)²
? = 1.22?/D
E = Z²*E1

28. Magnetic Field For Current in Long Wire
F = qv×B
µ0 I / 2pR
u dm/dt
ih_barL_z

29. Mech: Centripetal Force
U - ts = -tlog(Z)
F = mv²/r
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
F = I L X B

30. QM: de Broglie Wavelength
?= h/v(2mE)
1/ne - where n is charge carrier density
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
NC?T

31. Resonance frequency of LC circuit
I = -(c ?t)^2 + d^2
J = ? Fdt
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
1/vLC

32. td(entropy) =
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
E = <?| H |?>
PdV +dU
? = h/p

33. Energy levels from the Coulomb potential
? = 5/3
Dp/dt = L / (t ?V)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
E = <?| H |?>

34. Polarizers - intensity when crossed at ?
Z²/n² (m_red/m_elec)
dU = 0 ? dS = ?dW/T
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
I = I_0 Cos[?]^2

35. EM: Bremsstrahlung (translation)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Braking Radiation
U - ts = -tlog(Z)
?~T

36. Kepler'S Three Laws
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
C_eq = (? 1/C_i)^-1
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Cos[?] Sin[?] -Sin[?] Cos[?]

37. Relativistic Energy
?mc²
C_eq = ?C_i
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
?= h/v(2mE)

38. Rayleigh criterion
? = 1.22? / d
Faraday/Lenz: current inducted opposes the changing field
<T> = -<V>/2
NC?T

39. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
N²/Z (m_elec/m_red)
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
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

40. Perpendicular axis theorem
F = qv×B
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
I_z = I_x + I_y (think hoop symmetry)
W_A < W_I

41. Doppler Shift for light
S = k ln[O] ; dS = dQ/T
? = ?0 root((1-v/c)/(1+v/c))
Q = CVexp(-t/RC)
DW/dq

42. Force exerted on charge by long wire
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
F = µ0 q v I / 2pr
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
ih_barL_z

43. Quant: [L_x -L_y] = ?
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
ih_barL_z
dU = 0 ? dS = ?dW/T
qvb = mv²/R

44. Coriolis Force
Asin(?) = m?
F = -2*m(? x r)
1/vLC
1/2 CV²

45. Relativistic length contraction
Measurements close to mean
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
L = L_0 Sqrt[1-v^2/c^2]
?~T

46. Energy in a Capacitor
S = k ln[O] ; dS = dQ/T
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.
.5 CV²
I = I_0 Cos[?]^2

47. Lab: Standard Deviation of Poisson
? = 5/3
Opposing charge induced upon conductor
V = -L di/dt
v(mean)

48. EM: Reactance of Inductor
? = 5/3
F = R/2
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
X_L = i?L

49. Mech: Impulse
J = ? Fdt
S = k ln[O] ; dS = dQ/T
Hbar*?³/(p²c³exp(hbar?/t)-1)
Exponentially decreasing radial function

50. Pauli matrices
F = µ0 q v I / 2pr
4H + 2e- ? He +2? + 6?
?_max = b/T
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