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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. Weighted average (mean and unc. of mean)
F = -2*m(? x r)
I = -(c ?t)^2 + d^2
I ' = I cos²(?)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

2. Focal point of mirrror with curvature
F = R/2
C_eq = (? 1/C_i)^-1
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
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

3. Current in resistor in RC circuit
C_eq = ?C_i
I = V/R exp(-t/RC)
U - ts = -tlog(Z)
P/A = s T^4

4. Quant: Eigenvalue of Hermitian Operator
µ0 I1I2 / (2pd)
Cv = dE/dT = 3R
C = 4pe0 ab/(a-b) = inner and outer radii
Always Real

5. Atom: Bohr Formula
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
? = h/p
I = Im (sinc²(a)) ; a = pai sin(?) / ?
L = T - V dL/dq = d/dt dL/dqdot

6. Wein'S displacement law for blackbodies (? and T)
I ' = I cos²(?)
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.
?_max = b/T
?mv

7. Kepler'S third law (T and R)
µ = m_e/2
T^2 = k R^3 - k=constant
4H + 2e- ? He +2? + 6?
KE = 1/2 * µ (dr/dt)² L = µ r x v

8. EM: Electromagnetic inertia
Infinitely close to equilibrium at all times
?mc²
Faraday/Lenz: current inducted opposes the changing field
? = h/p

9. Bernoulli Equation
P +1/2 ? v² + ?gh = Constant
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
I = V/R exp(-t/RC)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

10. Partition Function
I = I_cm + (1/2)m d^2
B = µ0 I n
? exp(-e/t)
Z_c = -i/(?C) ; Z_L = i ? L

11. Lab: Standard Deviation of Poisson
v(mean)
F = f* (c+v_r)/(c+v_s)
I = I_0 Cos[?]^2
µ0 I / 2R

12. Electromotive Force
1/2 CV²
DW/dq
0
<T> = 1/2 * <dV/dx>

13. Rayleigh'S Criterion
dQ = dW +dU
Sin(?) = ?/d
NC?T
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

14. Magnetic Dipole Moment and Torque
X_C = 1/(i?C)
µ = Current * Area T = µ x B
?max = 2.898 x 10 -³ / T
V = -L di/dt

15. Malus Law

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16. Atom: Hydrogen Wave Function Type
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Sin(?) = ?/d
Exponentially decreasing radial function
1/2 CV²

17. Heat added
Exponentially decreasing radial function
NC?T
F_f = µ*F_N
P1V1 - P2V2 / (? - 1)

18. Anomalous Zeeman Effect

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19. Kepler'S Three Laws
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
J = ? Fdt

20. Error in the mean if each measurement has the same uncertainty s
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
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
S_mean = s/Sqrt[N]

21. Stark Effect
E = Z²*E1
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.
P² ~ R³
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

22. Parallel axis theorem
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
dQ = dW +dU
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.
I = I_cm + (1/2)m d^2

23. Solid: Resistivity of Metal
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
?~T
F = s * T4

24. Rocket Equation
Dv = -udm/m - v = v0 + u ln(m0/m)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
I = I_cm + (1/2)m d^2
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

25. Energy in Inductor
J = ? Fdt
.5 LI²
I ' = I cos²(?)
E = s/e_0

26. Internal Energy of an Ideal Gas
(3/2) n R ?t
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
T^2 = k R^3 - k=constant
X_L = i?L

27. Center of Mass: Kinetic Energy & Angular Momentum
I_z = I_x + I_y (think hoop symmetry)
<?1|?2> = 0 ? Orthogonal
N²/Z (m_elec/m_red)
KE = 1/2 * µ (dr/dt)² L = µ r x v

28. Thermo: Blackbody Radiation
Braking Radiation
F = s * T4
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
N d flux / dt

29. Delta Function Potential - type of WF
?mv
.5 LI²
P/A = s T^4
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

30. EM: Bremsstrahlung (translation)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
N²/Z (m_elec/m_red)
Braking Radiation
<?1|?2> = 0 ? Orthogonal

31. Commutator identities ( [B -A C] - [A -B] )
V = -L di/dt
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
.5 LI²

32. A reversible process stays..
Infinitely close to equilibrium at all times
ma + kx = 0
? (t-vx/c²)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

33. Single Slit Diffraction Intensity
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

34. Law of Mass Action
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
v(mean)
?mc²

35. Source-free RC Circuit
P/A = s T^4
µ = Current * Area T = µ x B
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
P1V1 - P2V2 / (? - 1)

36. Thermo: Isothermal
V(r) + L²2/2mr²
X_C = 1/(i?C)
dU = 0 ? dS = ?dW/T
Dv = -udm/m - v = v0 + u ln(m0/m)

37. Volumetric Expansion
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
<?1|?2> = 0 ? Orthogonal
V = V0 + V0 a ?T
J = E s - s = Conductivity - E = Electric field

38. Helmholtz Free Energy
DW/dq
U - ts = -tlog(Z)
S_mean = s/Sqrt[N]
Measurements close to mean

39. Rocket Thrust
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
V = V0 + V0 a ?T
U = t^2 d/dt (logZ)
u dm/dt

40. Induced EMF of solenoid
Exp(N(µ-e)/t)
N d flux / dt
0
ma + kx = 0

41. Quant: [L_x -L_y] = ?
ih_barL_z
v(mean)
Int ( A . dr) = Int ( del x A) dSurface
?_max = b/T

42. Atom: Positronium Reduced Mass
E = s/e_0
µ0 I1I2 / (2pd)
µ = m_e/2
I_z = I_x + I_y (think hoop symmetry)

43. EM: Maxwell'S equations
Measurements close to true value
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
NC?T
Z²/n² (m_red/m_elec)

44. Mech: Rotational Energy
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
I ' = I cos²(?)
T = I?²/2
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

45. Relativistic interval (which must remain constant for two events)
Dv = -udm/m - v = v0 + u ln(m0/m)
I = -(c ?t)^2 + d^2
NC?T
Braking Radiation

46. Relativistic Energy
?mc²
A[B -C] + [A -C]B
I = -(c ?t)^2 + d^2
Exponentially decreasing radial function

47. Bohr Model: Energy
Z²/n² (m_red/m_elec)
I = -(c ?t)^2 + d^2
Dv = -udm/m - v = v0 + u ln(m0/m)
ih_barL_z

48. Quant: Orthogonality of States
Dv = -udm/m - v = v0 + u ln(m0/m)
<?1|?2> = 0 ? Orthogonal
? = h/mv
u dm/dt

49. Polarizers - intensity when crossed at ?
I = V/R exp(-t/RC)
?mc²
I ' = I cos²(?)
I = I_0 Cos[?]^2

50. Astro: Aperture Formula (Rayleigh Criterion)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
? = 1.22?/D
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)