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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. Relativistic interval (which must remain constant for two events)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
µ = m_e/2
I = -(c ?t)^2 + d^2

2. Force on a wire in magnetic field
F = qv×B
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
KE = 1/2 * µ (dr/dt)² L = µ r x v
F = I L X B

3. Parallel axis theorem
I = I_cm + (1/2)m d^2
X_L = X_C or X_total = 0
dU = 0 ? dS = ?dW/T
?_max = b/T

4. Solid: Resistivity of Semi-Conductor
?~1/T
µ0 I / 2R
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
dU = 0 ? dS = ?dW/T

5. Doppler shift for light
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
.5 CV²
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.
V(r) + L²2/2mr²

6. Mech: Force of Friction
I ' = I cos²(?)
F_f = µ*F_N
Asin(?) = m?
S = k ln[O] ; dS = dQ/T

7. Malus Law

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8. Relativistic Energy
DW = P dV
?mc²
F = mv²/r
NC?T

9. A reversible process stays..
? = h/mv
Infinitely close to equilibrium at all times
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Isentropic

10. Rocket Equation
C_eq = ?C_i
Dv = -udm/m - v = v0 + u ln(m0/m)
Measurements close to true value
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

11. Gibbs Factor
T^2 = k R^3 - k=constant
I = I_cm + (1/2)m d^2
? = h/p
Exp(N(µ-e)/t)

12. Thermo: Monatomic gas ?=?
C_eq = (? 1/C_i)^-1
? = 5/3
F = f* (c+v_r)/(c+v_s)
X_L = X_C or X_total = 0

13. Anomalous Zeeman Effect

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14. Work done on a gas
Const: 2t = (n +.5)? Destructive 2t = n?
µ0 I / 2pR
DW = P dV
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

15. EM: Lorentz Force
C = 4pe0 ab/(a-b) = inner and outer radii
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
?mv
F = qv×B

16. Bragg'S Law of Reflection
M? = 2dsin(?)
µ0 I / 2R
F = R/2
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

17. QM: de Broglie Wavelength
?= h/v(2mE)
F = qv×B
DS = 0 - dQ = 0 - P V^? = constant
?? = h/mc * (1-cos(?))

18. Source-free RC Circuit
µ=s^2
E²-p²c²
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

19. EM: Reactance of Inductor
?= h/v(2mE)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
X_L = i?L

20. Rotation matrix (2x2)
? = 1.22? / d
µ0 I1I2 / (2pd)
µ0 I / 2R
Cos[?] Sin[?] -Sin[?] Cos[?]

21. Work in a capacitor
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
1/2 CV²
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
V(r) + L²2/2mr²

22. Commutator identities ( [B -A C] - [A -B] )
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?_max = b/T
u dm/dt
? = 5/3

23. Ohm'S Law w/ current density
DW = P dV
J = E s - s = Conductivity - E = Electric field
<?1|?2> = 0 ? Orthogonal
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.

24. Selection rules for atomic transitions
Z = ?g_i*exp(-E/kT)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
DW = P dV
Q = CVexp(-t/RC)

25. Relativistic length contraction
J/(ne) n: atom density
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Hbar*?³/(p²c³exp(hbar?/t)-1)
L = L_0 Sqrt[1-v^2/c^2]

26. Astro: Kepler'S Third Law
Braking Radiation
M? = 2dsin(?)
P² ~ R³
.5 CV²

27. Weighted average (mean and unc. of mean)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

28. Adiabatic processes (dS - dQ - P and V)
DS = 0 - dQ = 0 - P V^? = constant
Z²/n² (m_red/m_elec)
F = mv²/r
E = <?| H |?>

29. Center of Mass: Kinetic Energy & Angular Momentum
KE = 1/2 * µ (dr/dt)² L = µ r x v
dQ = dW +dU
Z = ?g_i*exp(-E/kT)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

30. Perpendicular axis theorem
X_L = X_C or X_total = 0
I_z = I_x + I_y (think hoop symmetry)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
? = 5/3

31. Stark Effect
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
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 = R/2
P +1/2 ? v² + ?gh = Constant

32. Mean electron drift speed
Ct²-x²-y²-z²
J/(ne) n: atom density
I = -(c ?t)^2 + d^2
T = I?²/2

33. Lab: Precision of Measurements
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.
V = -L di/dt
F = µ0 q v I / 2pr
Measurements close to mean

34. Invariant Energy Quantity
?mc²
? = ?0 root((1-v/c)/(1+v/c))
E²-p²c²
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

35. Inductance of Solenoid
S = k ln[O] ; dS = dQ/T
F = qv×B
M? = 2dsin(?)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

36. Astro: p-p Chain
?_max = b/T
4H + 2e- ? He +2? + 6?
.5 CV²
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

37. Rayleigh criterion
? = 5/3
U - ts = -tlog(Z)
Asin(?) = m?
? = 1.22? / d

38. Source Free RL Circuit
Always Real
Isentropic
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
V(r) + L²2/2mr²

39. Invariant spatial quantity
S_mean = s/Sqrt[N]
?~T
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Ct²-x²-y²-z²

40. Resonance frequency of LC circuit
1/vLC
0
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

41. Complex impedance (expressions for capacitor and inductor)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Z_c = -i/(?C) ; Z_L = i ? L
W_A < W_I
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

42. Coriolis Force
H = H_0 + ?H
F = -2*m(? x r)
DW = P dV
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

43. Kepler'S Three Laws
?s = 0 - ?l = ±1
A[B -C] + [A -C]B
L = L_0 Sqrt[1-v^2/c^2]
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

44. EM: Electromagnetic inertia
? (t-vx/c²)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
L = mr²d?/dt
Faraday/Lenz: current inducted opposes the changing field

45. E field of a capacitor (d->0)
L = L_0 Sqrt[1-v^2/c^2]
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
E = s/e_0
N²/Z (m_elec/m_red)

46. Poisson distribution (µ and s)
µ=s^2
P +1/2 ? v² + ?gh = Constant
ds² = (c*dt)² - ?(x_i)²
Const: 2t = (n +.5)? Destructive 2t = n?

47. Quant: [L_x -L_y] = ?
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
T^2 = k R^3 - k=constant
ih_barL_z

48. Boltzmann / Canonical distribution
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.
V = -L di/dt
F = s * T4
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

49. Energy in a Capacitor
M? = 2dsin(?)
Dv = -udm/m - v = v0 + u ln(m0/m)
.5 CV²
X_C = 1/(i?C)

50. Mech: Impulse
?~1/T
Dv = -udm/m - v = v0 + u ln(m0/m)
N d flux / dt
J = ? Fdt