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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Lagrangian and Lagrange'S equation
Isentropic
4H + 2e- ? He +2? + 6?
L = T - V dL/dq = d/dt dL/dqdot
U = t^2 d/dt (logZ)

2. De Broglie wavelength
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
? = h/p
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

3. Invariant spatial quantity
F = mv²/r
I = Im (sinc²(a)) ; a = pai sin(?) / ?
I ' = I cos²(?)
Ct²-x²-y²-z²

4. Doppler Shift for light
C = 4pe0 ab/(a-b) = inner and outer radii
? = ?0 root((1-v/c)/(1+v/c))
E = s/e_0
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

5. Spherical Capacitor Equation
C = 4pe0 ab/(a-b) = inner and outer radii
? (t-vx/c²)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Isentropic

6. Magnetic Field of a long solenoid
B = µ0 I n
C_eq = ?C_i
? = 1.22? / d
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.

7. Bohr Model: Energy
? = 1.22? / d
? = 5/3
Z²/n² (m_red/m_elec)
Exponentially decreasing radial function

8. Relativistic Energy
?mc²
J = ? Fdt
Dv = -udm/m - v = v0 + u ln(m0/m)
? exp(-e/t)

9. EM: Method of Images
Opposing charge induced upon conductor
I ' = I cos²(?)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
µ = m_e/2

10. Bohr Model: Radii
Q = CVexp(-t/RC)
N²/Z (m_elec/m_red)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
F = f* (c+v_r)/(c+v_s)

11. Stark Effect
µ = Current * Area T = µ x B
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
I = I_cm + (1/2)m d^2
C_eq = ?C_i

12. Hall Coefficient
1/ne - where n is charge carrier density
? exp(-e/t)
Dv = -udm/m - v = v0 + u ln(m0/m)
I = -(c ?t)^2 + d^2

13. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Cv = dE/dT = 3R
1/2 CV²
J/(ne) n: atom density

14. Stoke'S Theorem
? = h/mv
F = -2*m(? x r)
Braking Radiation
Int ( A . dr) = Int ( del x A) dSurface

15. Thermo: Average Total Energy
(° of Freedom)kT/2
?s = 0 - ?l = ±1
N²/Z (m_elec/m_red)
Infinitely close to equilibrium at all times

16. Magnetic Dipole Moment and Torque
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
µ = Current * Area T = µ x B
(3/2) n R ?t
DW/dq

17. Atom: Positronium Reduced Mass
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
µ = m_e/2
? = 1.22? / d
?s = 0 - ?l = ±1

18. Self Inductance
dQ = dW +dU
I = Im (sinc²(a)) ; a = pai sin(?) / ?
V = -L di/dt
.5 LI²

19. Mech: Parallel Axis Theorem (Moment of Inertia)
µ0 I / 2R
.5 LI²
I = I_cm + md²
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

20. Coriolis Force
Dp/dt = L / (t ?V)
Z_c = -i/(?C) ; Z_L = i ? L
F = -2*m(? x r)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

21. Heat added
M? = 2dsin(?)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
NC?T
P +1/2 ? v² + ?gh = Constant

22. EM: Lorentz Force
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Exp(N(µ-e)/t)
F = qv×B
L = T - V dL/dq = d/dt dL/dqdot

23. Quant: Orthogonality of States
T^2 = k R^3 - k=constant
<?1|?2> = 0 ? Orthogonal
? exp(-e/t)
E = <?| H |?>

24. Polarizers - intensity when crossed at ?
X_L = X_C or X_total = 0
?max = 2.898 x 10 -³ / T
I = I_0 Cos[?]^2
M? = 2dsin(?)

25. Force exerted on charge by long wire
F = µ0 q v I / 2pr
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
T^2 = k R^3 - k=constant
? exp(-e/t)

26. Bragg'S Law of Reflection
H = H_0 + ?H
N d flux / dt
X_C = 1/(i?C)
M? = 2dsin(?)

27. Lab: Accuracy of Measurements
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
L = T - V dL/dq = d/dt dL/dqdot
P1V1 - P2V2 / (? - 1)
Measurements close to true value

28. Magnetic Field Through Ring
µ0 I / 2R
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Cv = dE/dT = 3R
Z = ?g_i*exp(-E/kT)

29. Adiabatic means
Isentropic
?~T
DS = 0 - dQ = 0 - P V^? = constant
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

30. Resonance frequency of LC circuit
1/vLC
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.
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
I = Im (sinc²(a)) ; a = pai sin(?) / ?

31. Angular momentum operators L^2 and L_z
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
I_z = I_x + I_y (think hoop symmetry)
.5 CV²
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

32. Thermo: Adiabatic Work vs Isothermal Work
W_A < W_I
J = E s - s = Conductivity - E = Electric field
<T> = 1/2 * <dV/dx>
Braking Radiation

33. Solid: Resistivity of Metal
?~T
T = I?²/2
µ0 I / 2pR
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

34. Atom: Orbital Config
Z_c = -i/(?C) ; Z_L = i ? L
A[B -C] + [A -C]B
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
E = Z²*E1

35. Mech: Virial Theorem
Z²/n² (m_red/m_elec)
<T> = -<V>/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.
? = h/p

36. Boltzmann / Canonical distribution
P1V1 - P2V2 / (? - 1)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
A[B -C] + [A -C]B

37. Relativistic Momentum
? = 5/3
Dp/dt = L / (t ?V)
J/(ne) n: atom density
?mv

38. De Broigle Wavelength
E = <?| H |?>
ma + kx = 0
? = h/mv
I = -(c ?t)^2 + d^2

39. Parallel axis theorem
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
ma + kx = 0
I = I_cm + (1/2)m d^2
.5 LI²

40. Bar magnets -- direction of B field lines - earth'S B field
F = mv²/r
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
P +1/2 ? v² + ?gh = Constant
µ0 I / 2pR

41. Astro: Aperture Formula (Rayleigh Criterion)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
B = µ0 I n
? = 1.22?/D
F_f = µ*F_N

42. EM: Electromagnetic inertia
Infinitely close to equilibrium at all times
Cos[?] Sin[?] -Sin[?] Cos[?]
Faraday/Lenz: current inducted opposes the changing field
P1V1 - P2V2 / (? - 1)

43. Hamiltonian and Hamilton'S equations
Dp/dt = L / (t ?V)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
0
qvb = mv²/R

44. SR: Total Energy of a Particle
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
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
J = E s - s = Conductivity - E = Electric field
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

45. Inductance of Solenoid
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Dv = -udm/m - v = v0 + u ln(m0/m)
I ' = I cos²(?)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

46. Work (P - V)
P1V1 - P2V2 / (? - 1)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?mc²
KE = 1/2 * µ (dr/dt)² L = µ r x v

47. Magnetic Field For Current in Long Wire
Exponentially decreasing radial function
µ0 I / 2pR
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
µ=s^2

48. Virial Theorem
<T> = 1/2 * <dV/dx>
F = qv×B
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

49. EM: Reactance of Inductor
L = mr²d?/dt
X_L = i?L
J/(ne) n: atom density
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.

50. Source-free RC Circuit
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
Braking Radiation
I = I_cm + (1/2)m d^2
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)