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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. Atom: Positronium Reduced Mass
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
T^2 = k R^3 - k=constant
µ = m_e/2
? = ?0 root((1-v/c)/(1+v/c))

2. Work in a capacitor
1/2 CV²
?s = 0 - ?l = ±1
C = 4pe0 ab/(a-b) = inner and outer radii
(3/2) n R ?t

3. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
µ = m_e/2
I = Im (sinc²(a)) ; a = pai sin(?) / ?
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

4. Relativistic Energy
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
v(mean)
?mc²
F = mv²/r

5. SR: Total Energy of a Particle
dQ = dW +dU
Const: 2t = (n +.5)? Destructive 2t = n?
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

6. Solid: Resistivity of Semi-Conductor
L = T - V dL/dq = d/dt dL/dqdot
?~1/T
Z_c = -i/(?C) ; Z_L = i ? L
?? = h/mc * (1-cos(?))

7. Lensmaker Equation - Thin Lens
U - ts = -tlog(Z)
M? = 2dsin(?)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
µ=s^2

8. EM: Method of Images
Q = CVexp(-t/RC)
Opposing charge induced upon conductor
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
ih_barL_z

9. Perpendicular axis theorem
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
?= h/v(2mE)
I_z = I_x + I_y (think hoop symmetry)
L = mr²d?/dt

10. Kepler'S third law (T and R)
T^2 = k R^3 - k=constant
M? = 2dsin(?)
H = H_0 + ?H
µ = m_e/2

11. Angular momentum - Central Force Motion
0
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Measurements close to mean
L = mr²d?/dt

12. Ohm'S Law w/ current density
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
P/A = s T^4
I = Im (sinc²(a)) ; a = pai sin(?) / ?
J = E s - s = Conductivity - E = Electric field

13. Volumetric Expansion
KE = 1/2 * µ (dr/dt)² L = µ r x v
V = V0 + V0 a ?T
<T> = 1/2 * <dV/dx>
P² ~ R³

14. Pauli matrices
4H + 2e- ? He +2? + 6?
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
?mv
U - ts = -tlog(Z)

15. Mech: Virial Theorem
<T> = -<V>/2
.5 CV²
Z = ?g_i*exp(-E/kT)
?mv

16. Effective Potential
KE = 1/2 * µ (dr/dt)² L = µ r x v
? = 1.22? / d
V(r) + L²2/2mr²
DW = P dV

17. Mech: Centripetal Force
<?|O|?>
I = I_cm + (1/2)m d^2
F = mv²/r
Dv = -udm/m - v = v0 + u ln(m0/m)

18. Commutator identities ( [B -A C] - [A -B] )
Sin(?) = ?/d
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
NC?T

19. Astro: p-p Chain
C_eq = (? 1/C_i)^-1
4H + 2e- ? He +2? + 6?
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
ih_barL_z

20. Bohr Model: Energy
F = qv×B
Z²/n² (m_red/m_elec)
ih_barL_z
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

21. Energy levels from the Coulomb potential
dU = 0 ? dS = ?dW/T
I = I_0 Cos[?]^2
?mv
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

22. Partition Function
Dv = -udm/m - v = v0 + u ln(m0/m)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
? exp(-e/t)
U = t^2 d/dt (logZ)

23. EM: Reactance of Capacitor
? = h/p
X_C = 1/(i?C)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

24. RLC resonance condition
?~1/T
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I = -(c ?t)^2 + d^2
Braking Radiation

25. Expectation value of the energy of state |?>
F = µ0 q v I / 2pr
Hbar*?³/(p²c³exp(hbar?/t)-1)
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.
E = <?| H |?>

26. Mech: Parallel Axis Theorem (Moment of Inertia)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Hbar*?³/(p²c³exp(hbar?/t)-1)
B = µ0 I n
I = I_cm + md²

27. Triplet/singlet states: symmetry and net spin
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
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
X_L = i?L

28. Resonance frequency of LC circuit
Measurements close to true value
B = µ0 I n
1/vLC
Cv = dE/dT = 3R

29. Selection Rules
?s = 0 - ?l = ±1
C_eq = ?C_i
DW/dq
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

30. Invariant Energy Quantity
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
E²-p²c²
C_eq = (? 1/C_i)^-1
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

31. Gibbs Factor
W_A < W_I
E²-p²c²
Exp(N(µ-e)/t)
? = 1.22? / d

32. Stoke'S Theorem
?~1/T
Int ( A . dr) = Int ( del x A) dSurface
F = s * T4
X_C = 1/(i?C)

33. Rayleigh criterion
E = Z²*E1
?? = h/mc * (1-cos(?))
0
? = 1.22? / d

34. Work (P - V)
?? = h/mc * (1-cos(?))
v(mean)
P1V1 - P2V2 / (? - 1)
X_C = 1/(i?C)

35. Bragg'S Law of Reflection
?~T
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Ct²-x²-y²-z²
M? = 2dsin(?)

36. EM: Electromagnetic inertia
Measurements close to mean
Faraday/Lenz: current inducted opposes the changing field
<T> = -<V>/2
?_max = b/T

37. Thermo: Blackbody Radiation
U = t^2 d/dt (logZ)
F = s * T4
NC?T
?s = 0 - ?l = ±1

38. Energy in Inductor
Measurements close to true value
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
.5 LI²
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

39. Doppler shift for light
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Sin(?) = ?/d
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Measurements close to mean

40. EM: Electric Field inside of Conductor
I_z = I_x + I_y (think hoop symmetry)
0
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Opposing charge induced upon conductor

41. Center of Mass: Kinetic Energy & Angular Momentum
I ' = I cos²(?)
NC?T
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
KE = 1/2 * µ (dr/dt)² L = µ r x v

42. SR: Spacetime Interval
ds² = (c*dt)² - ?(x_i)²
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.
Sin(?) = ?/d
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

43. Spherical Capacitor Equation
C = 4pe0 ab/(a-b) = inner and outer radii
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
µ = m_e/2
dU = 0 ? dS = ?dW/T

44. Mech: Force of Friction
F_f = µ*F_N
<T> = 1/2 * <dV/dx>
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
M? = 2dsin(?)

45. Relativistic interval (which must remain constant for two events)
F = R/2
ma + kx = 0
N d flux / dt
I = -(c ?t)^2 + d^2

46. EM: AC Resonance
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)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
L = T - V dL/dq = d/dt dL/dqdot

47. Charge in Capacitor
Q = CVexp(-t/RC)
?~T
Measurements close to true value
DW = P dV

48. Compton Scattering
? = h/p
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
ih_barL_z
?? = h/mc * (1-cos(?))

49. Lagrangian and Lagrange'S equation
P² ~ R³
L = T - V dL/dq = d/dt dL/dqdot
? = ?0 root((1-v/c)/(1+v/c))
J/(ne) n: atom density

50. Helmholtz Free Energy
I = I_cm + md²
µ0 I / 2R
U - ts = -tlog(Z)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]