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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. Mech: Impulse
F = -2*m(? x r)
<T> = 1/2 * <dV/dx>
<T> = -<V>/2
J = ? Fdt

2. Clausius-Clapeyron Equation
F = mv²/r
Dp/dt = L / (t ?V)
Measurements close to mean
?s = 0 - ?l = ±1

3. Biot-Savart law
dQ = dW +dU
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
V = -L di/dt
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

4. Energy in terms of partition function
Infinitely close to equilibrium at all times
U = t^2 d/dt (logZ)
Faraday/Lenz: current inducted opposes the changing field
ds² = (c*dt)² - ?(x_i)²

5. Adiabatic processes (dS - dQ - P and V)
F = R/2
DS = 0 - dQ = 0 - P V^? = constant
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
<T> = -<V>/2

6. Mech: Centripetal Force
? = ?0 root((1-v/c)/(1+v/c))
I = -(c ?t)^2 + d^2
F = mv²/r
? = 1.22? / d

7. Solid: Resistivity of Semi-Conductor
J = E s - s = Conductivity - E = Electric field
?s = 0 - ?l = ±1
I_z = I_x + I_y (think hoop symmetry)
?~1/T

8. Kepler'S third law (T and R)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
I = Im (sinc²(a)) ; a = pai sin(?) / ?
T^2 = k R^3 - k=constant
Asin(?) = m?

9. QM: de Broglie Wavelength
Ct²-x²-y²-z²
?= h/v(2mE)
Measurements close to mean
? = 1.22? / d

10. Energy levels from the Coulomb potential
Infinitely close to equilibrium at all times
J = E s - s = Conductivity - E = Electric field
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

11. Source Free RL Circuit
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
P/A = s T^4

12. Complex impedance (expressions for capacitor and inductor)
Z_c = -i/(?C) ; Z_L = i ? L
?= h/v(2mE)
DW = P dV
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

13. Energy in a Capacitor
.5 CV²
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
? = 5/3
C = 4pe0 ab/(a-b) = inner and outer radii

14. Hamiltonian and Hamilton'S equations
P/A = s T^4
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Q = CVexp(-t/RC)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

15. Time Lorentz Transformation
? (t-vx/c²)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Always Real
N²/Z (m_elec/m_red)

16. Helmholtz Free Energy
F = R/2
I = -(c ?t)^2 + d^2
4H + 2e- ? He +2? + 6?
U - ts = -tlog(Z)

17. Angular momentum - Central Force Motion
? (t-vx/c²)
L = mr²d?/dt
J/(ne) n: atom density
U - ts = -tlog(Z)

18. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
H = H_0 + ?H
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

19. td(entropy) =
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?? = h/mc * (1-cos(?))
PdV +dU
F = I L X B

20. Delta Function Potential - type of WF
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
µ0 I / 2pR
.5 CV²
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

21. Solid: Resistivity of Metal
H = H_0 + ?H
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
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
?~T

22. Force on a wire in magnetic field
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Measurements close to true value
dU = 0 ? dS = ?dW/T
F = I L X B

23. Invariant spatial quantity
Z = ?g_i*exp(-E/kT)
Ct²-x²-y²-z²
B = µ0 I n
I = I_cm + md²

24. Work done on a gas
DW = P dV
I = I_0 Cos[?]^2
P² ~ R³
I = I_cm + (1/2)m d^2

25. EM: Electromagnetic inertia
Faraday/Lenz: current inducted opposes the changing field
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
(° of Freedom)kT/2
4H + 2e- ? He +2? + 6?

26. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
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.
I = I_cm + (1/2)m d^2
<T> = 1/2 * <dV/dx>

27. Coriolis Force
ma + kx = 0
4H + 2e- ? He +2? + 6?
?~T
F = -2*m(? x r)

28. Hall Coefficient
V(r) + L²2/2mr²
1/ne - where n is charge carrier density
? = h/p
? = 1.22?/D

29. Mean electron drift speed
Const: 2t = (n +.5)? Destructive 2t = n?
V = V0 + V0 a ?T
J/(ne) n: atom density
F_f = µ*F_N

30. RLC resonance condition
Q = CVexp(-t/RC)
S_mean = s/Sqrt[N]
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I = I_0 Cos[?]^2

31. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Cv = dE/dT = 3R
F_f = µ*F_N
U = t^2 d/dt (logZ)

32. Atom: Positronium Reduced Mass
µ = m_e/2
Z = ?g_i*exp(-E/kT)
Infinitely close to equilibrium at all times
1/ne - where n is charge carrier density

33. Parallel axis theorem
I = I_cm + (1/2)m d^2
Asin(?) = m?
Exp(N(µ-e)/t)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

34. Relativistic Energy
?_max = b/T
T = I?²/2
? = h/mv
?mc²

35. Magnetic Field Through Ring
Const: 2t = (n +.5)? Destructive 2t = n?
µ0 I / 2R
µ0 I / 2pR
4H + 2e- ? He +2? + 6?

36. EM: Method of Images
J = ? Fdt
J = E s - s = Conductivity - E = Electric field
?mc²
Opposing charge induced upon conductor

37. Magnetic Dipole Moment and Torque
?mc²
F = s * T4
µ = Current * Area T = µ x B
?mv

38. Bragg'S Law of Reflection
Measurements close to mean
M? = 2dsin(?)
Exp(N(µ-e)/t)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

39. Volumetric Expansion
V = -L di/dt
V = V0 + V0 a ?T
Always Real
E = s/e_0

40. EM: Electric Field inside of Conductor
V(r) + L²2/2mr²
0
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Measurements close to mean

41. Force/length between two wires
?? = h/mc * (1-cos(?))
? = h/mv
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
µ0 I1I2 / (2pd)

42. Magnetic field due to a segment of wire
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
F = qv×B
?_max = b/T
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

43. A reversible process stays..
Infinitely close to equilibrium at all times
? = h/p
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

44. Gibbs Factor
Cv = dE/dT = 3R
X_L = i?L
Dp/dt = L / (t ?V)
Exp(N(µ-e)/t)

45. Angular momentum operators L^2 and L_z
µ = Current * Area T = µ x B
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
X_L = X_C or X_total = 0
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

46. Adiabatic means
T = I?²/2
.5 LI²
Isentropic
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

47. Electromotive Force
DW/dq
F = s * T4
? = 5/3
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

48. Error in the mean if each measurement has the same uncertainty s
Z_c = -i/(?C) ; Z_L = i ? L
<?1|?2> = 0 ? Orthogonal
S_mean = s/Sqrt[N]
P1V1 - P2V2 / (? - 1)

49. De Broigle Wavelength
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
? = h/mv
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
I = I_0 Cos[?]^2

50. Resistance - length - area - rho
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Cv = dE/dT = 3R
J/(ne) n: atom density