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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. Springs in series/parallel
µ0 I / 2R
X_L = i?L
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

2. Thermo: Partition Function
Z = ?g_i*exp(-E/kT)
?= h/v(2mE)
I = -(c ?t)^2 + d^2
Ct²-x²-y²-z²

3. EM: Electromagnetic inertia
Z = ?g_i*exp(-E/kT)
Faraday/Lenz: current inducted opposes the changing field
C_eq = ?C_i
F_f = µ*F_N

4. Magnetic Field of a long solenoid
Z_c = -i/(?C) ; Z_L = i ? L
B = µ0 I n
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

5. Stark Effect
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
u dm/dt
N d flux / dt
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

6. Effective Potential
Z²/n² (m_red/m_elec)
E²-p²c²
u dm/dt
V(r) + L²2/2mr²

7. Anomalous Zeeman Effect

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8. Self Inductance
J = E s - s = Conductivity - E = Electric field
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
V = -L di/dt

9. Resonance frequency of LC circuit
W_A < W_I
F = R/2
?s = 0 - ?l = ±1
1/vLC

10. Bohr Model: Radii
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
N²/Z (m_elec/m_red)

11. Work in a capacitor
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
dU = 0 ? dS = ?dW/T
1/2 CV²
1/ne - where n is charge carrier density

12. Lab: Precision of Measurements
Isentropic
Measurements close to mean
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
4H + 2e- ? He +2? + 6?

13. EM: Method of Images
Opposing charge induced upon conductor
N²/Z (m_elec/m_red)
(3/2) n R ?t
0

14. SR: Spacetime Interval
? = 1.22?/D
B = µ0 I n
I = I_cm + md²
ds² = (c*dt)² - ?(x_i)²

15. Virial Theorem
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
<T> = 1/2 * <dV/dx>
µ=s^2
C_eq = ?C_i

16. Energy in terms of partition function
(° of Freedom)kT/2
U = t^2 d/dt (logZ)
L = T - V dL/dq = d/dt dL/dqdot
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

17. Magnetic Field For Current in Long Wire
<?1|?2> = 0 ? Orthogonal
µ0 I / 2pR
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

18. Hall Coefficient
PdV +dU
1/ne - where n is charge carrier density
Asin(?) = m?
L = L_0 Sqrt[1-v^2/c^2]

19. Electromotive Force
?s = 0 - ?l = ±1
DW/dq
µ = Current * Area T = µ x B
F = R/2

20. Invariant Energy Quantity
E²-p²c²
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
<T> = -<V>/2
? exp(-e/t)

21. Single Slit Diffraction Intensity
<?1|?2> = 0 ? Orthogonal
? = 1.22?/D
DS = 0 - dQ = 0 - P V^? = constant
I = Im (sinc²(a)) ; a = pai sin(?) / ?

22. Parallel axis theorem
I = I_cm + (1/2)m d^2
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
? = h/mv
H = H_0 + ?H

23. De Broglie wavelength
? = h/p
F = -2*m(? x r)
Cv = dE/dT = 3R
Z²/n² (m_red/m_elec)

24. Bar magnets -- direction of B field lines - earth'S B field
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Z = ?g_i*exp(-E/kT)
I_z = I_x + I_y (think hoop symmetry)
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

25. Bohr Model: Energy
(° of Freedom)kT/2
u dm/dt
Z²/n² (m_red/m_elec)
?mc²

26. EM: Series Capacitance
N d flux / dt
C_eq = (? 1/C_i)^-1
H = H_0 + ?H
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

27. Work (P - V)
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.
T = I?²/2
P1V1 - P2V2 / (? - 1)
I = I_0 Cos[?]^2

28. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
Z_c = -i/(?C) ; Z_L = i ? L
Infinitely close to equilibrium at all times
F_f = µ*F_N

29. Doppler shift for light
T^2 = k R^3 - k=constant
F = qv×B
I = Im (sinc²(a)) ; a = pai sin(?) / ?
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

30. Entropy (# of states - and in terms of other thermo quantities)
? (t-vx/c²)
J = ? Fdt
A[B -C] + [A -C]B
S = k ln[O] ; dS = dQ/T

31. Energy in a Capacitor
C = 4pe0 ab/(a-b) = inner and outer radii
µ=s^2
.5 CV²
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

32. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
E = Z²*E1
DS = 0 - dQ = 0 - P V^? = constant
?mv

33. Mech: Virial Theorem
<T> = -<V>/2
µ=s^2
S = k ln[O] ; dS = dQ/T
Isentropic

34. Dulong Petit Law
Cv = dE/dT = 3R
?~1/T
W_A < W_I
L = mr²d?/dt

35. Thermo: Monatomic gas ?=?
? = 5/3
Isentropic
DW/dq
ih_barL_z

36. Current in resistor in RC circuit
?~T
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
I = V/R exp(-t/RC)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

37. Inductance of Solenoid
DS = 0 - dQ = 0 - P V^? = constant
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
F = qv×B
4H + 2e- ? He +2? + 6?

38. Bernoulli Equation
X_C = 1/(i?C)
W_A < W_I
P +1/2 ? v² + ?gh = Constant
dQ = dW +dU

39. EM: Reactance of Capacitor
X_C = 1/(i?C)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Braking Radiation
? = h/p

40. Relativistic Momentum
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
?mv
F = s * T4

41. Atom: Orbital Config
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
E = s/e_0
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
?mv

42. Malus Law

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43. Adiabatic processes (dS - dQ - P and V)
E = s/e_0
<?1|?2> = 0 ? Orthogonal
DS = 0 - dQ = 0 - P V^? = constant
NC?T

44. Solid: Resistivity of Semi-Conductor
F_f = µ*F_N
V = -L di/dt
?~1/T
<T> = -<V>/2

45. Gibbs Factor
<?1|?2> = 0 ? Orthogonal
F_f = µ*F_N
Exp(N(µ-e)/t)
P² ~ R³

46. Angular momentum operators L^2 and L_z
(3/2) n R ?t
S_mean = s/Sqrt[N]
v(mean)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

47. Thermo: Blackbody Radiation
ds² = (c*dt)² - ?(x_i)²
DS = 0 - dQ = 0 - P V^? = constant
F = s * T4
Q = CVexp(-t/RC)

48. EM: AC Resonance
X_L = X_C or X_total = 0
?~T
?? = h/mc * (1-cos(?))
X_L = i?L

49. Commutator identities ( [B -A C] - [A -B] )
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = mv²/r
N d flux / dt
T^2 = k R^3 - k=constant

50. EM: Bremsstrahlung (translation)
? = ?0 root((1-v/c)/(1+v/c))
Braking Radiation
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
P +1/2 ? v² + ?gh = Constant