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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. Bohr Model: Radii
N²/Z (m_elec/m_red)
U = t^2 d/dt (logZ)
ds² = (c*dt)² - ?(x_i)²
Q = CVexp(-t/RC)

2. Perpendicular axis theorem
I_z = I_x + I_y (think hoop symmetry)
? = ?0 root((1-v/c)/(1+v/c))
T = I?²/2
? = h/mv

3. Quant: Orthogonality of States
<?1|?2> = 0 ? Orthogonal
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Dp/dt = L / (t ?V)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

4. Internal Energy of an Ideal Gas
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
C_eq = ?C_i
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
(3/2) n R ?t

5. Weighted average (mean and unc. of mean)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Q = CVexp(-t/RC)
ds² = (c*dt)² - ?(x_i)²
U - ts = -tlog(Z)

6. RLC resonance condition
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Cv = dE/dT = 3R
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
ih_barL_z

7. Angular momentum - Central Force Motion
L = mr²d?/dt
? = 1.22?/D
X_L = X_C or X_total = 0
?~T

8. Single Slit Diffraction Maximum
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
F = I L X B
Asin(?) = m?
F = qv×B

9. Force exerted on charge by long wire
F = µ0 q v I / 2pr
I = I_0 Cos[?]^2
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
<T> = 1/2 * <dV/dx>

10. Astro: Kepler'S Third Law
P² ~ R³
Z = ?g_i*exp(-E/kT)
B = µ0 I n
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

11. Hall Coefficient
1/ne - where n is charge carrier density
? = h/p
V = -L di/dt
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

12. Adiabatic means
Z = ?g_i*exp(-E/kT)
Isentropic
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
F = s * T4

13. EM: Reactance of Inductor
I = I_cm + md²
X_L = i?L
W_A < W_I
DS = 0 - dQ = 0 - P V^? = constant

14. Lagrangian and Lagrange'S equation
1/vLC
ih_barL_z
4H + 2e- ? He +2? + 6?
L = T - V dL/dq = d/dt dL/dqdot

15. Magnetic field due to a segment of wire
F = µ0 q v I / 2pr
?mv
I = Im (sinc²(a)) ; a = pai sin(?) / ?
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

16. Inductance of Solenoid
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
A[B -C] + [A -C]B
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
V = -L di/dt

17. Quant: [L_x -L_y] = ?
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
ih_barL_z
X_L = i?L

18. Mech: Impulse
I ' = I cos²(?)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
I = I_cm + (1/2)m d^2
J = ? Fdt

19. How to derive cylcotron frequency
qvb = mv²/R
DW = P dV
F = mv²/r
µ = m_e/2

20. Heat added
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
4H + 2e- ? He +2? + 6?
Dp/dt = L / (t ?V)
NC?T

21. Source Free RL Circuit
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Cos[?] Sin[?] -Sin[?] Cos[?]
L = mr²d?/dt
Opposing charge induced upon conductor

22. Source-free RC Circuit
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
4H + 2e- ? He +2? + 6?
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

23. Springs in series/parallel
Hbar*?³/(p²c³exp(hbar?/t)-1)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
µ = m_e/2
S = k ln[O] ; dS = dQ/T

24. Center of Mass: Kinetic Energy & Angular Momentum
KE = 1/2 * µ (dr/dt)² L = µ r x v
?? = h/mc * (1-cos(?))
J = E s - s = Conductivity - E = Electric field
(3/2) n R ?t

25. Stoke'S Theorem
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
µ=s^2
Int ( A . dr) = Int ( del x A) dSurface
X_L = X_C or X_total = 0

26. EM: Method of Images
? (t-vx/c²)
C_eq = ?C_i
Dv = -udm/m - v = v0 + u ln(m0/m)
Opposing charge induced upon conductor

27. Coriolis Force
M? = 2dsin(?)
qvb = mv²/R
E²-p²c²
F = -2*m(? x r)

28. Magnetic Dipole Moment and Torque
I = I_cm + md²
F = f* (c+v_r)/(c+v_s)
<?|O|?>
µ = Current * Area T = µ x B

29. Commutator identities ( [B -A C] - [A -B] )
? = 5/3
Z²/n² (m_red/m_elec)
E = <?| H |?>
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

30. Spherical Capacitor Equation
F = I L X B
C = 4pe0 ab/(a-b) = inner and outer radii
F = qv×B
Sin(?) = ?/d

31. Wein'S displacement law for blackbodies (? and T)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
.5 LI²
?_max = b/T
B = µ0 I n

32. Thermo: Monatomic gas ?=?
<?1|?2> = 0 ? Orthogonal
U = t^2 d/dt (logZ)
? = 5/3
Cos[?] Sin[?] -Sin[?] Cos[?]

33. Mech: Virial Theorem
Cv = dE/dT = 3R
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
<T> = -<V>/2
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

34. Partition Function
? exp(-e/t)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
0

35. Mech: Rotational Energy
T = I?²/2
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
E = Z²*E1
C_eq = ?C_i

36. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Z = ?g_i*exp(-E/kT)
dU = 0 ? dS = ?dW/T

37. Bernoulli Equation
Q = CVexp(-t/RC)
P +1/2 ? v² + ?gh = Constant
µ = Current * Area T = µ x B
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

38. Quant: Commutator Relation [AB -C]
? (t-vx/c²)
A[B -C] + [A -C]B
I = Im (sinc²(a)) ; a = pai sin(?) / ?
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

39. Lensmaker Equation - Thin Lens
I ' = I cos²(?)
Dv = -udm/m - v = v0 + u ln(m0/m)
NC?T
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

40. Polarizers - intensity when crossed at ?
F = µ0 q v I / 2pr
I = I_0 Cos[?]^2
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

41. Work (P - V)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Z = ?g_i*exp(-E/kT)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
P1V1 - P2V2 / (? - 1)

42. Thermo: Average Total Energy
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Const: 2t = (n +.5)? Destructive 2t = n?
(° of Freedom)kT/2
M? = 2dsin(?)

43. Bohr Model: Energy
Faraday/Lenz: current inducted opposes the changing field
1/ne - where n is charge carrier density
KE = 1/2 * µ (dr/dt)² L = µ r x v
Z²/n² (m_red/m_elec)

44. EM: AC Resonance
X_L = X_C or X_total = 0
F = µ0 q v I / 2pr
J = E s - s = Conductivity - E = Electric field
.5 LI²

45. EM: Bremsstrahlung (translation)
DW = P dV
Braking Radiation
I = I_cm + (1/2)m d^2
I ' = I cos²(?)

46. Energy in Inductor
.5 LI²
C = 4pe0 ab/(a-b) = inner and outer radii
T = I?²/2
Opposing charge induced upon conductor

47. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
.5 CV²
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
NC?T

48. Radiation (Larmor - and another neat fact)
F_f = µ*F_N
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
P/A = s T^4
u dm/dt

49. Biot-Savart law
Opposing charge induced upon conductor
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
Braking Radiation

50. Lab: Accuracy of Measurements
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
Measurements close to true value
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i