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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
? = ?0 root((1-v/c)/(1+v/c))
L = L_0 Sqrt[1-v^2/c^2]
J = ? Fdt
Z²/n² (m_red/m_elec)

2. Mean electron drift speed
J/(ne) n: atom density
U - ts = -tlog(Z)
Cos[?] Sin[?] -Sin[?] Cos[?]
F = qv×B

3. How to derive cylcotron frequency
µ = m_e/2
qvb = mv²/R
Dp/dt = L / (t ?V)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

4. Energy levels from the Coulomb potential
ds² = (c*dt)² - ?(x_i)²
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Measurements close to mean
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

5. Addition of relativistic velocities

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6. Pauli matrices
J = ? Fdt
Measurements close to mean
KE = 1/2 * µ (dr/dt)² L = µ r x v
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

7. Wein'S displacement law for blackbodies (? and T)
?_max = b/T
µ0 I / 2R
I = I_0 Cos[?]^2
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

8. Stoke'S Theorem
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Int ( A . dr) = Int ( del x A) dSurface
L = T - V dL/dq = d/dt dL/dqdot
I = I_cm + (1/2)m d^2

9. Anomalous Zeeman Effect

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10. Bohr Model: Radii
Ct²-x²-y²-z²
Braking Radiation
N²/Z (m_elec/m_red)
Dp/dt = L / (t ?V)

11. Delta Function Potential - type of WF
F = I L X B
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.
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

12. Spherical Capacitor Equation
F = µ0 q v I / 2pr
V(r) + L²2/2mr²
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
C = 4pe0 ab/(a-b) = inner and outer radii

13. Bar magnets -- direction of B field lines - earth'S B field
DW/dq
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 = -2*m(? x r)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

14. Mech: Rotational Energy
Exp(N(µ-e)/t)
I = V/R exp(-t/RC)
? = 1.22? / d
T = I?²/2

15. Doppler Shift in Frequency
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
W_A < W_I
F = f* (c+v_r)/(c+v_s)
ih_barL_z

16. Rayleigh criterion
I = -(c ?t)^2 + d^2
S = k ln[O] ; dS = dQ/T
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
? = 1.22? / d

17. Wein'S Displacement Law
qvb = mv²/R
?max = 2.898 x 10 -³ / T
?= h/v(2mE)
?s = 0 - ?l = ±1

18. Lab: Standard Deviation of Poisson
Opposing charge induced upon conductor
v(mean)
E = <?| H |?>
?mc²

19. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
M? = 2dsin(?)
DW = P dV
.5 CV²

20. Thermo: Adiabatic Work vs Isothermal Work
F = R/2
W_A < W_I
Ct²-x²-y²-z²
? = 5/3

21. Source-free RC Circuit
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
?~1/T
? (t-vx/c²)

22. Invariant Energy Quantity
M? = 2dsin(?)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
E²-p²c²
?~T

23. Boltzmann / Canonical distribution
NC?T
Exp(N(µ-e)/t)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
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.

24. Springs in series/parallel
µ0 I / 2pR
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
F = R/2
F = s * T4

25. Perpendicular axis theorem
? (t-vx/c²)
I = -(c ?t)^2 + d^2
E = <?| H |?>
I_z = I_x + I_y (think hoop symmetry)

26. Inductance of Solenoid
J/(ne) n: atom density
H = H_0 + ?H
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
1/vLC

27. EM: Bremsstrahlung (translation)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
dU = 0 ? dS = ?dW/T
Braking Radiation
?= h/v(2mE)

28. Double Slit: Interference Minimum - Diffraction Minimum
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
J/(ne) n: atom density
? = h/mv
E = Z²*E1

29. EM: Reactance of Inductor
X_L = i?L
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
µ = m_e/2
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

30. Magnetic Field of a long solenoid
B = µ0 I n
P +1/2 ? v² + ?gh = Constant
?? = h/mc * (1-cos(?))
u dm/dt

31. Angular momentum operators L^2 and L_z
(3/2) n R ?t
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
F = µ0 q v I / 2pr

32. Expectation value of the energy of state |?>
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Dv = -udm/m - v = v0 + u ln(m0/m)
v(mean)
E = <?| H |?>

33. Perturbations
ds² = (c*dt)² - ?(x_i)²
Z = ?g_i*exp(-E/kT)
Always Real
H = H_0 + ?H

34. Bragg'S Law of Reflection
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
M? = 2dsin(?)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
? = 1.22?/D

35. Biot-Savart law
A[B -C] + [A -C]B
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
F = -2*m(? x r)
µ0 I / 2R

36. Adiabatic means
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Isentropic
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
PdV +dU

37. Bernoulli Equation
V = -L di/dt
P +1/2 ? v² + ?gh = Constant
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
(° of Freedom)kT/2

38. Magnetic Field For Current in Long Wire
U = t^2 d/dt (logZ)
Z²/n² (m_red/m_elec)
µ0 I / 2pR
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

39. Malus Law

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40. Source Free RL Circuit
I = Im (sinc²(a)) ; a = pai sin(?) / ?
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
ds² = (c*dt)² - ?(x_i)²
ma + kx = 0

41. Stark Effect
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
<?1|?2> = 0 ? Orthogonal
Ct²-x²-y²-z²
E = <?| H |?>

42. Atom: Orbital Config
Z = ?g_i*exp(-E/kT)
<T> = -<V>/2
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
NC?T

43. EM: Electromagnetic inertia
Faraday/Lenz: current inducted opposes the changing field
I = Im (sinc²(a)) ; a = pai sin(?) / ?
?~1/T
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

44. Commutator identities ( [B -A C] - [A -B] )
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
J/(ne) n: atom density
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

45. Rocket Equation
Opposing charge induced upon conductor
Dv = -udm/m - v = v0 + u ln(m0/m)
J = ? Fdt
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

46. Heat added
P² ~ R³
<?1|?2> = 0 ? Orthogonal
u dm/dt
NC?T

47. Dulong Petit Law
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Cv = dE/dT = 3R
N²/Z (m_elec/m_red)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

48. Relativistic Energy
Dv = -udm/m - v = v0 + u ln(m0/m)
? = 1.22?/D
ds² = (c*dt)² - ?(x_i)²
?mc²

49. Rayleigh'S Criterion
C_eq = (? 1/C_i)^-1
I = -(c ?t)^2 + d^2
Sin(?) = ?/d
E²-p²c²

50. Stefan-Boltzmann law for blackbodies (power per area and T)
P/A = s T^4
?mv
?~1/T
µ=s^2