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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. Rotation matrix (2x2)
? (t-vx/c²)
qvb = mv²/R
? exp(-e/t)
Cos[?] Sin[?] -Sin[?] Cos[?]

2. Bohr Model: Energy
1/vLC
Z²/n² (m_red/m_elec)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

3. EM: Parallel Capacitance
?? = h/mc * (1-cos(?))
µ0 I / 2pR
B = µ0 I n
C_eq = ?C_i

4. Energy levels from the Coulomb potential
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
I = I_0 Cos[?]^2
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

5. Magnetic field due to a segment of wire
I = -(c ?t)^2 + d^2
.5 CV²
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
F = s * T4

6. Quant: Orthogonality of States
µ0 I / 2R
C_eq = ?C_i
<?1|?2> = 0 ? Orthogonal
(3/2) n R ?t

7. De Broglie wavelength
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
? = h/p
Dv = -udm/m - v = v0 + u ln(m0/m)
X_C = 1/(i?C)

8. EM: Reactance of Inductor
X_L = i?L
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Dp/dt = L / (t ?V)
? = h/mv

9. Partition Function
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
? exp(-e/t)
Opposing charge induced upon conductor
I = I_cm + md²

10. Double Slit: Interference Minimum - Diffraction Minimum
?_max = b/T
(° of Freedom)kT/2
?mc²
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

11. EM: SHO (Hooke)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
ma + kx = 0
P/A = s T^4
Int ( A . dr) = Int ( del x A) dSurface

12. Thermo: Average Total Energy
(° of Freedom)kT/2
Cos[?] Sin[?] -Sin[?] Cos[?]
F_f = µ*F_N
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

13. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
S_mean = s/Sqrt[N]
? (t-vx/c²)
KE = 1/2 * µ (dr/dt)² L = µ r x v

14. Clausius-Clapeyron Equation
Dp/dt = L / (t ?V)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Z_c = -i/(?C) ; Z_L = i ? L
Dv = -udm/m - v = v0 + u ln(m0/m)

15. Force exerted on charge by long wire
F = µ0 q v I / 2pr
Opposing charge induced upon conductor
PdV +dU
µ0 I1I2 / (2pd)

16. Solid: Resistivity of Metal
Always Real
? = 5/3
1/vLC
?~T

17. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Const: 2t = (n +.5)? Destructive 2t = n?
I_z = I_x + I_y (think hoop symmetry)

18. Thermo: 1st Law
dQ = dW +dU
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
E = Z²*E1
Sin(?) = ?/d

19. Quant: [L_x -L_y] = ?
ih_barL_z
1/2 CV²
Dv = -udm/m - v = v0 + u ln(m0/m)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

20. Kepler'S third law (T and R)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Q = CVexp(-t/RC)
T^2 = k R^3 - k=constant
?max = 2.898 x 10 -³ / T

21. Commutator identities ( [B -A C] - [A -B] )
I_z = I_x + I_y (think hoop symmetry)
Cos[?] Sin[?] -Sin[?] Cos[?]
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?_max = b/T

22. Mech: Virial Theorem
? = ?0 root((1-v/c)/(1+v/c))
V = -L di/dt
E = Z²*E1
<T> = -<V>/2

23. Invariant spatial quantity
Ct²-x²-y²-z²
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.
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

24. Thermo: Partition Function
Opposing charge induced upon conductor
? = 1.22?/D
Z = ?g_i*exp(-E/kT)
I = V/R exp(-t/RC)

25. Gibbs Factor
U - ts = -tlog(Z)
Braking Radiation
Exp(N(µ-e)/t)
F = f* (c+v_r)/(c+v_s)

26. EM: Bremsstrahlung (translation)
Always Real
F_f = µ*F_N
Braking Radiation
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

27. Bohr Model: Radii
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
A[B -C] + [A -C]B
N²/Z (m_elec/m_red)
Faraday/Lenz: current inducted opposes the changing field

28. Parallel axis theorem
I = I_cm + (1/2)m d^2
?~T
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
I = -(c ?t)^2 + d^2

29. Resistance - length - area - rho
F = µ0 q v I / 2pr
Cv = dE/dT = 3R
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
4H + 2e- ? He +2? + 6?

30. De Broigle Wavelength
?_max = b/T
? = h/mv
(° of Freedom)kT/2
ds² = (c*dt)² - ?(x_i)²

31. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Cv = dE/dT = 3R
1/2 CV²

32. Single Slit Diffraction Intensity
I_z = I_x + I_y (think hoop symmetry)
I = Im (sinc²(a)) ; a = pai sin(?) / ?
E = s/e_0
?_max = b/T

33. Mech: Parallel Axis Theorem (Moment of Inertia)
E = Z²*E1
P1V1 - P2V2 / (? - 1)
I ' = I cos²(?)
I = I_cm + md²

34. Compton Scattering
I = Im (sinc²(a)) ; a = pai sin(?) / ?
µ0 I1I2 / (2pd)
?? = h/mc * (1-cos(?))
C_eq = ?C_i

35. Mean electron drift speed
? = 1.22?/D
J/(ne) n: atom density
? = 1.22? / d
? = 5/3

36. Mech: Centripetal Force
? = 5/3
F = mv²/r
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_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

37. Work done on a gas
ds² = (c*dt)² - ?(x_i)²
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.
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
DW = P dV

38. Thermo: Blackbody Radiation
Measurements close to true value
µ0 I1I2 / (2pd)
Asin(?) = m?
F = s * T4

39. Addition of relativistic velocities

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40. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
.5 LI²
I = I_0 Cos[?]^2
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

41. Magnetic Field of a long solenoid
B = µ0 I n
V(r) + L²2/2mr²
Infinitely close to equilibrium at all times
F = -2*m(? x r)

42. Work in a capacitor
1/2 CV²
E = Z²*E1
µ=s^2
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

43. Thermo: Monatomic gas ?=?
<?|O|?>
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
v(mean)
? = 5/3

44. Volumetric Expansion
N²/Z (m_elec/m_red)
V = V0 + V0 a ?T
Faraday/Lenz: current inducted opposes the changing field
µ = m_e/2

45. Radiation (Larmor - and another neat fact)
Sin(?) = ?/d
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

46. Atom: Bohr Theory Ionization
Braking Radiation
E = Z²*E1
?max = 2.898 x 10 -³ / T
? (t-vx/c²)

47. Thermo: Isothermal
?mc²
W_A < W_I
I = I_cm + (1/2)m d^2
dU = 0 ? dS = ?dW/T

48. Expectation value of the energy of state |?>
L = T - V dL/dq = d/dt dL/dqdot
E = <?| H |?>
µ=s^2
Hbar*?³/(p²c³exp(hbar?/t)-1)

49. Relativistic length contraction
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
µ = m_e/2
L = L_0 Sqrt[1-v^2/c^2]
Ct²-x²-y²-z²

50. Current in resistor in RC circuit
ds² = (c*dt)² - ?(x_i)²
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
I = V/R exp(-t/RC)
J = ? Fdt