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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. How to derive cylcotron frequency
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
ih_barL_z
qvb = mv²/R
L = mr²d?/dt

2. EM: Maxwell'S equations
L = T - V dL/dq = d/dt dL/dqdot
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

3. Malus Law

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4. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
M? = 2dsin(?)

5. Doppler shift for light
<T> = 1/2 * <dV/dx>
?~T
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
DW = P dV

6. E field of a capacitor (d->0)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
E = s/e_0
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
.5 LI²

7. Bernoulli Equation
C_eq = ?C_i
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
Z = ?g_i*exp(-E/kT)
P +1/2 ? v² + ?gh = Constant

8. Atom: Bohr Theory Ionization
Cos[?] Sin[?] -Sin[?] Cos[?]
J = ? Fdt
E = Z²*E1
<?|O|?>

9. Parallel axis theorem
?_max = b/T
? exp(-e/t)
I = I_cm + (1/2)m d^2
.5 CV²

10. Thin Film Theory: Constructive / Destructive Interference
I = I_cm + md²
Const: 2t = (n +.5)? Destructive 2t = n?
I ' = I cos²(?)
(° of Freedom)kT/2

11. Boltzmann / Canonical distribution
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
µ0 I1I2 / (2pd)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

12. Lab: Precision of Measurements
KE = 1/2 * µ (dr/dt)² L = µ r x v
Measurements close to mean
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
S = k ln[O] ; dS = dQ/T

13. Induced EMF of solenoid
L = mr²d?/dt
L = T - V dL/dq = d/dt dL/dqdot
N d flux / dt
µ = Current * Area T = µ x B

14. SR: Total Energy of a Particle
µ0 I / 2R
? = 5/3
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
V = V0 + V0 a ?T

15. Thermo: Monatomic gas ?=?
? (t-vx/c²)
? = 5/3
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
E = Z²*E1

16. Energy in Inductor
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
.5 LI²
µ=s^2
J = ? Fdt

17. Anomalous Zeeman Effect

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18. Source Free RL Circuit
.5 LI²
Exp(N(µ-e)/t)
I_z = I_x + I_y (think hoop symmetry)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

19. Adiabatic means
? = 1.22? / d
Isentropic
C_eq = (? 1/C_i)^-1
?mv

20. Addition of relativistic velocities

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21. Mech: Centripetal Force
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
T^2 = k R^3 - k=constant
Always Real
F = mv²/r

22. Energy in a Capacitor
S = k ln[O] ; dS = dQ/T
.5 CV²
N d flux / dt
?? = h/mc * (1-cos(?))

23. Single Slit Diffraction Intensity
µ0 I / 2pR
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Infinitely close to equilibrium at all times
Cv = dE/dT = 3R

24. Internal Energy of an Ideal Gas
4H + 2e- ? He +2? + 6?
µ=s^2
(3/2) n R ?t
Int ( A . dr) = Int ( del x A) dSurface

25. Thermo: Average Total Energy
F = f* (c+v_r)/(c+v_s)
Q = CVexp(-t/RC)
(° of Freedom)kT/2
?? = h/mc * (1-cos(?))

26. Quant: Expectation Value
<?|O|?>
<T> = -<V>/2
Measurements close to true value
1/2 CV²

27. Lagrangian and Lagrange'S equation
µ0 I1I2 / (2pd)
L = T - V dL/dq = d/dt dL/dqdot
?~1/T
F = mv²/r

28. Hamiltonian and Hamilton'S equations
DS = 0 - dQ = 0 - P V^? = constant
T = I?²/2
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
1/ne - where n is charge carrier density

29. Lensmaker Equation - Thin Lens
DS = 0 - dQ = 0 - P V^? = constant
Isentropic
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
<T> = -<V>/2

30. Dulong Petit Law
Measurements close to mean
? (t-vx/c²)
µ=s^2
Cv = dE/dT = 3R

31. Relativistic interval (which must remain constant for two events)
I = -(c ?t)^2 + d^2
Cos[?] Sin[?] -Sin[?] Cos[?]
E = Z²*E1
P² ~ R³

32. RLC resonance condition
0
Z²/n² (m_red/m_elec)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
U - ts = -tlog(Z)

33. Angular momentum - Central Force Motion
J/(ne) n: atom density
L = mr²d?/dt
Z²/n² (m_red/m_elec)
? = 5/3

34. Partition Function
Ct²-x²-y²-z²
ma + kx = 0
? exp(-e/t)
DW/dq

35. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
E = <?| H |?>
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

36. EM: Reactance of Capacitor
X_C = 1/(i?C)
P1V1 - P2V2 / (? - 1)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

37. Complex impedance (expressions for capacitor and inductor)
Z_c = -i/(?C) ; Z_L = i ? L
u dm/dt
P +1/2 ? v² + ?gh = Constant
C_eq = ?C_i

38. Stark Effect
Exp(N(µ-e)/t)
I = V/R exp(-t/RC)
(3/2) n R ?t
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

39. Law of Mass Action
E = Z²*E1
Const: 2t = (n +.5)? Destructive 2t = n?
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

40. QM: de Broglie Wavelength
PdV +dU
F = qv×B
?s = 0 - ?l = ±1
?= h/v(2mE)

41. Commutator identities ( [B -A C] - [A -B] )
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Z = ?g_i*exp(-E/kT)

42. EM: Bremsstrahlung (translation)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Braking Radiation
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
W_A < W_I

43. De Broglie wavelength
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
? = h/p
µ=s^2
DS = 0 - dQ = 0 - P V^? = constant

44. Thermo: 1st Law
µ0 I / 2pR
µ0 I / 2R
Cv = dE/dT = 3R
dQ = dW +dU

45. Compton Scattering
ih_barL_z
? = 1.22? / d
?? = h/mc * (1-cos(?))
C = 4pe0 ab/(a-b) = inner and outer radii

46. Adiabatic processes (dS - dQ - P and V)
Braking Radiation
DS = 0 - dQ = 0 - P V^? = constant
DW/dq
Asin(?) = m?

47. Thermo: Blackbody Radiation
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
F = s * T4
W_A < W_I
V = V0 + V0 a ?T

48. Self Inductance
V = -L di/dt
DS = 0 - dQ = 0 - P V^? = constant
Int ( A . dr) = Int ( del x A) dSurface
<?1|?2> = 0 ? Orthogonal

49. Radiation (Larmor - and another neat fact)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F = -2*m(? x r)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
H = H_0 + ?H

50. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
F = s * T4
?? = h/mc * (1-cos(?))
L = mr²d?/dt