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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. E field of a capacitor (d->0)
<?|O|?>
1/2 CV²
.5 CV²
E = s/e_0

2. Virial Theorem
qvb = mv²/R
<T> = 1/2 * <dV/dx>
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
E = s/e_0

3. Resistance - length - area - rho
Always Real
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Asin(?) = m?

4. Partition Function
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Dp/dt = L / (t ?V)
? exp(-e/t)
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

5. Lagrangian and Lagrange'S equation
P1V1 - P2V2 / (? - 1)
L = T - V dL/dq = d/dt dL/dqdot
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
U - ts = -tlog(Z)

6. Stoke'S Theorem
µ0 I1I2 / (2pd)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Int ( A . dr) = Int ( del x A) dSurface
<T> = -<V>/2

7. Thermo: 1st Law
u dm/dt
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
dQ = dW +dU
Cv = dE/dT = 3R

8. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_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.
V(r) + L²2/2mr²
L = mr²d?/dt

9. Thermo: Isothermal
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
C_eq = ?C_i
dU = 0 ? dS = ?dW/T

10. De Broglie wavelength
Infinitely close to equilibrium at all times
?? = h/mc * (1-cos(?))
? = h/p
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

11. Delta Function Potential - type of WF
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Z²/n² (m_red/m_elec)
E²-p²c²
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

12. Effective Potential
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
I = I_0 Cos[?]^2
DW = P dV
V(r) + L²2/2mr²

13. Angular momentum - Central Force Motion
L = mr²d?/dt
Cos[?] Sin[?] -Sin[?] Cos[?]
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
u dm/dt

14. Single Slit Diffraction Intensity
C_eq = ?C_i
P1V1 - P2V2 / (? - 1)
J/(ne) n: atom density
I = Im (sinc²(a)) ; a = pai sin(?) / ?

15. Induced EMF of solenoid
N²/Z (m_elec/m_red)
? (t-vx/c²)
N d flux / dt
W_A < W_I

16. Thermo: Partition Function
Z = ?g_i*exp(-E/kT)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
F = -2*m(? x r)
I = -(c ?t)^2 + d^2

17. EM: AC Resonance
X_L = X_C or X_total = 0
Braking Radiation
J = ? Fdt
(° of Freedom)kT/2

18. Atom: Orbital Config
Isentropic
<T> = 1/2 * <dV/dx>
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
? = ?0 root((1-v/c)/(1+v/c))

19. Mech: Force of Friction
<?1|?2> = 0 ? Orthogonal
F_f = µ*F_N
.5 CV²
F = mv²/r

20. Compton Scattering
V = V0 + V0 a ?T
Dp/dt = L / (t ?V)
C_eq = (? 1/C_i)^-1
?? = h/mc * (1-cos(?))

21. EM: SHO (Hooke)
<?1|?2> = 0 ? Orthogonal
N²/Z (m_elec/m_red)
ma + kx = 0
Always Real

22. Angular momentum operators L^2 and L_z
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
µ0 I / 2pR
? = h/p
F = s * T4

23. Thermo: Adiabatic Work vs Isothermal Work
KE = 1/2 * µ (dr/dt)² L = µ r x v
?max = 2.898 x 10 -³ / T
Z²/n² (m_red/m_elec)
W_A < W_I

24. Quant: Eigenvalue of Hermitian Operator
Always Real
P² ~ R³
.5 CV²
F = mv²/r

25. Energy in a Capacitor
.5 CV²
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
F = mv²/r

26. Doppler shift for light
DW/dq
E = <?| H |?>
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

27. Internal Energy of an Ideal Gas
I = I_cm + (1/2)m d^2
.5 CV²
DW = P dV
(3/2) n R ?t

28. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
1/ne - where n is charge carrier density
C_eq = (? 1/C_i)^-1

29. Weighted average (mean and unc. of mean)
Asin(?) = m?
Const: 2t = (n +.5)? Destructive 2t = n?
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
F_f = µ*F_N

30. Energy in terms of partition function
C_eq = (? 1/C_i)^-1
ma + kx = 0
U = t^2 d/dt (logZ)
E = s/e_0

31. Solid: Resistivity of Semi-Conductor
N d flux / dt
? = ?0 root((1-v/c)/(1+v/c))
?~1/T
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

32. Planck Radiation Law
P² ~ R³
Hbar*?³/(p²c³exp(hbar?/t)-1)
L = mr²d?/dt
Dv = -udm/m - v = v0 + u ln(m0/m)

33. How to derive cylcotron frequency
Isentropic
qvb = mv²/R
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
E = <?| H |?>

34. Radiation (Larmor - and another neat fact)
? = ?0 root((1-v/c)/(1+v/c))
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
L = T - V dL/dq = d/dt dL/dqdot
?_max = b/T

35. Thermo: Average Total Energy
1/2 CV²
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
(° of Freedom)kT/2
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

36. Heat added
1/ne - where n is charge carrier density
4H + 2e- ? He +2? + 6?
NC?T
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

37. Expectation value of the energy of state |?>
I = V/R exp(-t/RC)
Measurements close to mean
Infinitely close to equilibrium at all times
E = <?| H |?>

38. EM: Reactance of Capacitor
<T> = 1/2 * <dV/dx>
C = 4pe0 ab/(a-b) = inner and outer radii
E = Z²*E1
X_C = 1/(i?C)

39. Malus Law

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40. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
v(mean)
X_L = X_C or X_total = 0
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

41. Biot-Savart law
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
E = s/e_0
DW = P dV
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

42. Bohr Model: Radii
N²/Z (m_elec/m_red)
µ = Current * Area T = µ x B
M? = 2dsin(?)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

43. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
µ0 I / 2pR
0
F_f = µ*F_N

44. Lab: Standard Deviation of Poisson
Dv = -udm/m - v = v0 + u ln(m0/m)
v(mean)
Z_c = -i/(?C) ; Z_L = i ? L
Exp(N(µ-e)/t)

45. Electromotive Force
Braking Radiation
L = L_0 Sqrt[1-v^2/c^2]
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
DW/dq

46. Wein'S Displacement Law
ih_barL_z
?max = 2.898 x 10 -³ / T
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
?s = 0 - ?l = ±1

47. EM: Electric Field inside of Conductor
U = t^2 d/dt (logZ)
0
?= h/v(2mE)
Asin(?) = m?

48. Adiabatic means
? = ?0 root((1-v/c)/(1+v/c))
W_A < W_I
C = 4pe0 ab/(a-b) = inner and outer radii
Isentropic

49. Self Inductance
J/(ne) n: atom density
T^2 = k R^3 - k=constant
V = -L di/dt
Isentropic

50. Bar magnets -- direction of B field lines - earth'S B field
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
DW = P dV
<?|O|?>