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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. Mech: Centripetal Force
F = mv²/r
I = I_0 Cos[?]^2
DW = P dV
v(mean)

2. Inductance of Solenoid
?s = 0 - ?l = ±1
µ0 I1I2 / (2pd)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

3. Biot-Savart law
Z²/n² (m_red/m_elec)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
C_eq = ?C_i
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

4. Internal Energy of an Ideal Gas
N²/Z (m_elec/m_red)
Dv = -udm/m - v = v0 + u ln(m0/m)
(3/2) n R ?t
F = I L X B

5. Atom: Positronium Reduced Mass
µ0 I / 2pR
0
V = -L di/dt
µ = m_e/2

6. Work done on a gas
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
B = µ0 I n
DW = P dV
Z²/n² (m_red/m_elec)

7. EM: SHO (Hooke)
ma + kx = 0
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
dQ = dW +dU
C_eq = ?C_i

8. td(entropy) =
L = mr²d?/dt
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
?mc²
PdV +dU

9. Quant: [L_x -L_y] = ?
S_mean = s/Sqrt[N]
Exponentially decreasing radial function
ih_barL_z
F = µ0 q v I / 2pr

10. Self Inductance
DS = 0 - dQ = 0 - P V^? = constant
V = -L di/dt
T^2 = k R^3 - k=constant
? (t-vx/c²)

11. Energy in a Capacitor
I = I_0 Cos[?]^2
?mv
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
.5 CV²

12. Work (P - V)
I ' = I cos²(?)
I_z = I_x + I_y (think hoop symmetry)
P1V1 - P2V2 / (? - 1)
DS = 0 - dQ = 0 - P V^? = constant

13. Magnetic Field of a long solenoid
B = µ0 I n
?= h/v(2mE)
I = -(c ?t)^2 + d^2
W_A < W_I

14. Compton Scattering
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
F = R/2
M? = 2dsin(?)
?? = h/mc * (1-cos(?))

15. Mech: Virial Theorem
<T> = -<V>/2
.5 LI²
?? = h/mc * (1-cos(?))
N d flux / dt

16. Selection rules for atomic transitions
I = I_cm + (1/2)m d^2
Int ( A . dr) = Int ( del x A) dSurface
? exp(-e/t)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

17. Thermo: Adiabatic Work vs Isothermal Work
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?max = 2.898 x 10 -³ / T
µ = m_e/2
W_A < W_I

18. Rocket Thrust
Ct²-x²-y²-z²
(3/2) n R ?t
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
u dm/dt

19. E field of a capacitor (d->0)
v(mean)
E = s/e_0
?_max = b/T
DW = P dV

20. EM: Method of Images
Opposing charge induced upon conductor
?~1/T
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
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.

21. Quant: Eigenvalue of Hermitian Operator
F = qv×B
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Always Real
?_max = b/T

22. SR: Spacetime Interval
Measurements close to mean
ds² = (c*dt)² - ?(x_i)²
I = V/R exp(-t/RC)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

23. Stefan-Boltzmann law for blackbodies (power per area and T)
P² ~ R³
<?|O|?>
1/vLC
P/A = s T^4

24. Astro: p-p Chain
T^2 = k R^3 - k=constant
4H + 2e- ? He +2? + 6?
F = qv×B
N d flux / dt

25. EM: Electromagnetic inertia
Faraday/Lenz: current inducted opposes the changing field
.5 LI²
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

26. Electromotive Force
µ0 I1I2 / (2pd)
DW/dq
?= h/v(2mE)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

27. Bohr Model: Energy
(° of Freedom)kT/2
P1V1 - P2V2 / (? - 1)
Z²/n² (m_red/m_elec)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

28. Pauli matrices
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
I_z = I_x + I_y (think hoop symmetry)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
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

29. Magnetic field due to a segment of wire
L = mr²d?/dt
N²/Z (m_elec/m_red)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Z_c = -i/(?C) ; Z_L = i ? L

30. Single Slit Diffraction Maximum
Cos[?] Sin[?] -Sin[?] Cos[?]
A[B -C] + [A -C]B
KE = 1/2 * µ (dr/dt)² L = µ r x v
Asin(?) = m?

31. Quant: Expectation Value
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
N²/Z (m_elec/m_red)
<?|O|?>
A[B -C] + [A -C]B

32. Mech: Parallel Axis Theorem (Moment of Inertia)
I_z = I_x + I_y (think hoop symmetry)
T = I?²/2
E²-p²c²
I = I_cm + md²

33. EM: Reactance of Inductor
X_L = i?L
J = E s - s = Conductivity - E = Electric field
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
J/(ne) n: atom density

34. Commutator identities ( [B -A C] - [A -B] )
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
<?|O|?>
X_C = 1/(i?C)
?_max = b/T

35. Hamiltonian and Hamilton'S equations
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
v(mean)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Cv = dE/dT = 3R

36. Triplet/singlet states: symmetry and net spin
Dp/dt = L / (t ?V)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
X_L = X_C or X_total = 0

37. Mech: Force of Friction
F_f = µ*F_N
E²-p²c²
µ = m_e/2
P1V1 - P2V2 / (? - 1)

38. EM: Bremsstrahlung (translation)
Braking Radiation
dU = 0 ? dS = ?dW/T
T = I?²/2
Z = ?g_i*exp(-E/kT)

39. EM: Electric Field inside of Conductor
Cos[?] Sin[?] -Sin[?] Cos[?]
0
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Z²/n² (m_red/m_elec)

40. Entropy (# of states - and in terms of other thermo quantities)
S = k ln[O] ; dS = dQ/T
I = V/R exp(-t/RC)
I_z = I_x + I_y (think hoop symmetry)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

41. Stark Effect
0
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
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
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.

42. Current in resistor in RC circuit
F = µ0 q v I / 2pr
I = V/R exp(-t/RC)
Braking Radiation
F = qv×B

43. Virial Theorem
V = V0 + V0 a ?T
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
I = I_cm + md²
<T> = 1/2 * <dV/dx>

44. EM: Reactance of Capacitor
I = I_cm + md²
U - ts = -tlog(Z)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
X_C = 1/(i?C)

45. Lagrangian and Lagrange'S equation
Ct²-x²-y²-z²
L = T - V dL/dq = d/dt dL/dqdot
F = I L X B
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

46. Thermo: Isothermal
T^2 = k R^3 - k=constant
N d flux / dt
DW/dq
dU = 0 ? dS = ?dW/T

47. Quant: Commutator Relation [AB -C]
A[B -C] + [A -C]B
Measurements close to true value
X_C = 1/(i?C)
µ0 I / 2pR

48. Expectation value of the energy of state |?>
J = E s - s = Conductivity - E = Electric field
Z = ?g_i*exp(-E/kT)
E = <?| H |?>
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

49. Quant: Orthogonality of States
<?1|?2> = 0 ? Orthogonal
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
E = Z²*E1
E²-p²c²

50. Helmholtz Free Energy
U - ts = -tlog(Z)
Sin(?) = ?/d
Cos[?] Sin[?] -Sin[?] Cos[?]
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration