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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. Quant: Eigenvalue of Hermitian Operator
I ' = I cos²(?)
Always Real
S_mean = s/Sqrt[N]
0

2. Charge in Capacitor
Exp(N(µ-e)/t)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
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
Q = CVexp(-t/RC)

3. Wein'S Displacement Law
F = R/2
?max = 2.898 x 10 -³ / T
C = 4pe0 ab/(a-b) = inner and outer radii
ds² = (c*dt)² - ?(x_i)²

4. Coriolis Force
1/2 CV²
F = -2*m(? x r)
F = mv²/r
F = R/2

5. Relativistic Energy
X_C = 1/(i?C)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
?mc²

6. Lab: Standard Deviation of Poisson
Exp(N(µ-e)/t)
v(mean)
Z²/n² (m_red/m_elec)
µ0 I1I2 / (2pd)

7. Self Inductance
V = -L di/dt
P² ~ R³
?_max = b/T
Exponentially decreasing radial function

8. How to derive cylcotron frequency
qvb = mv²/R
Z²/n² (m_red/m_elec)
L = L_0 Sqrt[1-v^2/c^2]
4H + 2e- ? He +2? + 6?

9. Rayleigh'S Criterion
Exp(N(µ-e)/t)
Z_c = -i/(?C) ; Z_L = i ? L
Ct²-x²-y²-z²
Sin(?) = ?/d

10. EM: Parallel Capacitance
F = I L X B
C_eq = ?C_i
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
F = mv²/r

11. Quant: Expectation Value
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
0
<?|O|?>
F = I L X B

12. Magnetic Dipole Moment and Torque
µ = Current * Area T = µ x B
ds² = (c*dt)² - ?(x_i)²
I = Im (sinc²(a)) ; a = pai sin(?) / ?
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

13. Center of Mass: Kinetic Energy & Angular Momentum
Z²/n² (m_red/m_elec)
ma + kx = 0
X_C = 1/(i?C)
KE = 1/2 * µ (dr/dt)² L = µ r x v

14. Mean electron drift speed
X_L = i?L
?_max = b/T
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
J/(ne) n: atom density

15. Doppler shift for light
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 = Z²*E1
I = -(c ?t)^2 + d^2
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

16. EM: Bremsstrahlung (translation)
Braking Radiation
dU = 0 ? dS = ?dW/T
Measurements close to mean
A[B -C] + [A -C]B

17. Volumetric Expansion
<T> = -<V>/2
V = V0 + V0 a ?T
.5 LI²
I_z = I_x + I_y (think hoop symmetry)

18. Mech: Impulse
P1V1 - P2V2 / (? - 1)
F = mv²/r
.5 LI²
J = ? Fdt

19. Gibbs Factor
Sin(?) = ?/d
B = µ0 I n
X_C = 1/(i?C)
Exp(N(µ-e)/t)

20. EM: Electric Field inside of Conductor
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
M? = 2dsin(?)
0
F = f* (c+v_r)/(c+v_s)

21. Invariant spatial quantity
DW = P dV
I_z = I_x + I_y (think hoop symmetry)
? = h/mv
Ct²-x²-y²-z²

22. Mech: Virial Theorem
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Hbar*?³/(p²c³exp(hbar?/t)-1)
F = mv²/r
<T> = -<V>/2

23. Lab: Accuracy of Measurements
Measurements close to true value
I ' = I cos²(?)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Z_c = -i/(?C) ; Z_L = i ? L

24. Doppler Shift for light
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Exponentially decreasing radial function
M? = 2dsin(?)
? = ?0 root((1-v/c)/(1+v/c))

25. RLC resonance condition
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
NC?T
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

26. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
<T> = -<V>/2
DW = P dV

27. E field of a capacitor (d->0)
Dv = -udm/m - v = v0 + u ln(m0/m)
.5 LI²
E = s/e_0
Dp/dt = L / (t ?V)

28. EM: Electromagnetic inertia
Faraday/Lenz: current inducted opposes the changing field
T = I?²/2
I ' = I cos²(?)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

29. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
KE = 1/2 * µ (dr/dt)² L = µ r x v
P/A = s T^4
A[B -C] + [A -C]B

30. Clausius-Clapeyron Equation
M? = 2dsin(?)
L = T - V dL/dq = d/dt dL/dqdot
Dp/dt = L / (t ?V)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

31. Energy levels from the Coulomb potential
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
<T> = 1/2 * <dV/dx>
L = mr²d?/dt

32. QM: de Broglie Wavelength
?= h/v(2mE)
µ = Current * Area T = µ x B
(3/2) n R ?t
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

33. Resistance - length - area - rho
? exp(-e/t)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
? = 1.22? / d
E²-p²c²

34. Rocket Thrust
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
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.
X_L = X_C or X_total = 0
u dm/dt

35. Weighted average (mean and unc. of mean)
? (t-vx/c²)
B = µ0 I n
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

36. Force on a wire in magnetic field
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
ih_barL_z
F = I L X B
? (t-vx/c²)

37. Polarizers - intensity when crossed at ?
Isentropic
Dp/dt = L / (t ?V)
I = I_0 Cos[?]^2
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

38. Current in resistor in RC circuit
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
J/(ne) n: atom density
J = E s - s = Conductivity - E = Electric field
I = V/R exp(-t/RC)

39. Angular momentum operators L^2 and L_z
ih_barL_z
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Sin(?) = ?/d
Exp(N(µ-e)/t)

40. Mech: Parallel Axis Theorem (Moment of Inertia)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
I = I_cm + md²
µ = Current * Area T = µ x B
? = 5/3

41. Relativistic Momentum
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
?mv
F = I L X B
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

42. Thermo: Blackbody Radiation
Opposing charge induced upon conductor
S = k ln[O] ; dS = dQ/T
F = s * T4
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

43. Bohr Model: Energy
Z²/n² (m_red/m_elec)
(3/2) n R ?t
? = h/p
Hbar*?³/(p²c³exp(hbar?/t)-1)

44. Law of Mass Action
N²/Z (m_elec/m_red)
C_eq = (? 1/C_i)^-1
Braking Radiation
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

45. Energy in a Capacitor
H = H_0 + ?H
4H + 2e- ? He +2? + 6?
.5 CV²
Opposing charge induced upon conductor

46. Adiabatic means
? = 5/3
I_z = I_x + I_y (think hoop symmetry)
Isentropic
F = µ0 q v I / 2pr

47. Spherical Capacitor Equation
u dm/dt
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
C = 4pe0 ab/(a-b) = inner and outer radii
P +1/2 ? v² + ?gh = Constant

48. Thermo: Isothermal
<T> = -<V>/2
M? = 2dsin(?)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
dU = 0 ? dS = ?dW/T

49. Time Lorentz Transformation
1/vLC
? = h/mv
Opposing charge induced upon conductor
? (t-vx/c²)

50. Mech: Centripetal Force
DS = 0 - dQ = 0 - P V^? = constant
F = mv²/r
X_L = i?L
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2