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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. Effective Potential
V(r) + L²2/2mr²
F_f = µ*F_N
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
µ=s^2

2. Mech: Force of Friction
F = -2*m(? x r)
F_f = µ*F_N
I ' = I cos²(?)
L = mr²d?/dt

3. Quant: Orthogonality of States
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Measurements close to true value
<?1|?2> = 0 ? Orthogonal
<T> = 1/2 * <dV/dx>

4. Compton Scattering
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?? = h/mc * (1-cos(?))
(° of Freedom)kT/2
F = mv²/r

5. Focal point of mirrror with curvature
A[B -C] + [A -C]B
F = R/2
C_eq = ?C_i
? = 1.22? / d

6. Selection rules for atomic transitions
dU = 0 ? dS = ?dW/T
µ = Current * Area T = µ x B
U = t^2 d/dt (logZ)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

7. Work in a capacitor
Ct²-x²-y²-z²
P² ~ R³
µ = Current * Area T = µ x B
1/2 CV²

8. Virial Theorem
? (t-vx/c²)
dU = 0 ? dS = ?dW/T
<T> = 1/2 * <dV/dx>
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

9. Bohr Model: Radii
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
N d flux / dt
N²/Z (m_elec/m_red)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

10. Single Slit Diffraction Maximum
Faraday/Lenz: current inducted opposes the changing field
Cv = dE/dT = 3R
Asin(?) = m?
Int ( A . dr) = Int ( del x A) dSurface

11. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Measurements close to mean
E = s/e_0

12. Atom: Hydrogen Wave Function Type
I = I_cm + md²
Dv = -udm/m - v = v0 + u ln(m0/m)
?~T
Exponentially decreasing radial function

13. EM: Maxwell'S equations
V = V0 + V0 a ?T
PdV +dU
C = 4pe0 ab/(a-b) = inner and outer radii
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

14. Lab: Standard Deviation of Poisson
V = -L di/dt
v(mean)
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.
qvb = mv²/R

15. Wein'S displacement law for blackbodies (? and T)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
0
DS = 0 - dQ = 0 - P V^? = constant
?_max = b/T

16. EM: Reactance of Inductor
Int ( A . dr) = Int ( del x A) dSurface
X_L = i?L
L = L_0 Sqrt[1-v^2/c^2]
U - ts = -tlog(Z)

17. Coriolis Force
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = -2*m(? x r)
E = <?| H |?>
F = I L X B

18. QM: de Broglie Wavelength
F = -2*m(? x r)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?= h/v(2mE)
I = I_cm + md²

19. Mech: Centripetal Force
F = f* (c+v_r)/(c+v_s)
Z²/n² (m_red/m_elec)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
F = mv²/r

20. Commutator identities ( [B -A C] - [A -B] )
I = I_cm + (1/2)m d^2
Faraday/Lenz: current inducted opposes the changing field
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
ih_barL_z

21. Triplet/singlet states: symmetry and net spin
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.
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
<T> = 1/2 * <dV/dx>

22. Work (P - V)
S = k ln[O] ; dS = dQ/T
V = V0 + V0 a ?T
P1V1 - P2V2 / (? - 1)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

23. Single Slit Diffraction Intensity
<?1|?2> = 0 ? Orthogonal
P1V1 - P2V2 / (? - 1)
I = Im (sinc²(a)) ; a = pai sin(?) / ?
E = s/e_0

24. Helmholtz Free Energy
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
U - ts = -tlog(Z)
Isentropic
µ0 I1I2 / (2pd)

25. Quant: Eigenvalue of Hermitian Operator
µ=s^2
X_L = X_C or X_total = 0
V = -L di/dt
Always Real

26. Doppler shift for light
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
1/vLC
?~1/T
µ=s^2

27. Biot-Savart law
? = 5/3
Z²/n² (m_red/m_elec)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
?~T

28. EM: Lorentz Force
F = qv×B
N d flux / dt
Dp/dt = L / (t ?V)
?? = h/mc * (1-cos(?))

29. Atom: Orbital Config
µ0 I / 2pR
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
L = L_0 Sqrt[1-v^2/c^2]

30. Polarizers - intensity when crossed at ?
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
? (t-vx/c²)
I = I_0 Cos[?]^2
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

31. Heat added
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
NC?T

32. EM: Series Capacitance
I = -(c ?t)^2 + d^2
C_eq = (? 1/C_i)^-1
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

33. Law of Mass Action
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
u dm/dt
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
F_f = µ*F_N

34. Magnetic Field Through Ring
N²/Z (m_elec/m_red)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
µ0 I / 2R

35. EM: Electric Field inside of Conductor
X_L = X_C or X_total = 0
DS = 0 - dQ = 0 - P V^? = constant
µ = Current * Area T = µ x B
0

36. Stark Effect
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
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
C = 4pe0 ab/(a-b) = inner and outer radii
Cos[?] Sin[?] -Sin[?] Cos[?]

37. Solid: Resistivity of Metal
µ0 I / 2R
?~T
V = -L di/dt
J = ? Fdt

38. Mech: Rotational Energy
F = µ0 q v I / 2pr
T = I?²/2
L = mr²d?/dt
H = H_0 + ?H

39. Lagrangian and Lagrange'S equation
Always Real
?s = 0 - ?l = ±1
DW/dq
L = T - V dL/dq = d/dt dL/dqdot

40. Quant: [L_x -L_y] = ?
ih_barL_z
u dm/dt
E = <?| H |?>
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

41. Magnetic Dipole Moment and Torque
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
PdV +dU
µ = Current * Area T = µ x B

42. Magnetic Field For Current in Long Wire
Dv = -udm/m - v = v0 + u ln(m0/m)
µ0 I / 2pR
Asin(?) = m?
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

43. EM: Reactance of Capacitor
Z = ?g_i*exp(-E/kT)
X_C = 1/(i?C)
?_max = b/T
dQ = dW +dU

44. EM: Method of Images
µ0 I / 2R
S_mean = s/Sqrt[N]
Opposing charge induced upon conductor
Cv = dE/dT = 3R

45. Volumetric Expansion
? = h/mv
0
V = V0 + V0 a ?T
F = mv²/r

46. EM: Parallel Capacitance
C_eq = ?C_i
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
I = I_cm + md²

47. Force exerted on charge by long wire
F = µ0 q v I / 2pr
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Always Real
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

48. EM: SHO (Hooke)
C_eq = (? 1/C_i)^-1
ma + kx = 0
<T> = -<V>/2
(3/2) n R ?t

49. First law of thermodynamics (explain direction of energy for each term)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
V = V0 + V0 a ?T
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
P +1/2 ? v² + ?gh = Constant

50. Parallel axis theorem
I = I_cm + (1/2)m d^2
?mv
F_f = µ*F_N
I ' = I cos²(?)