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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. Resonance frequency of LC circuit
(3/2) n R ?t
1/vLC
E²-p²c²
(° of Freedom)kT/2

2. Work (P - V)
P1V1 - P2V2 / (? - 1)
F = f* (c+v_r)/(c+v_s)
E²-p²c²
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

3. Selection Rules
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
F = f* (c+v_r)/(c+v_s)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
?s = 0 - ?l = ±1

4. Atom: Hydrogen Wave Function Type
Exp(N(µ-e)/t)
Exponentially decreasing radial function
U = t^2 d/dt (logZ)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

5. Internal Energy of an Ideal Gas
? = 5/3
.5 LI²
Braking Radiation
(3/2) n R ?t

6. Delta Function Potential - type of WF
I = I_0 Cos[?]^2
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Always Real
ma + kx = 0

7. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
<T> = -<V>/2
dQ = dW +dU

8. Spherical Capacitor Equation
C = 4pe0 ab/(a-b) = inner and outer radii
A[B -C] + [A -C]B
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

9. Lagrangian and Lagrange'S equation
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
L = T - V dL/dq = d/dt dL/dqdot
F_f = µ*F_N
Isentropic

10. Volumetric Expansion
V = V0 + V0 a ?T
Measurements close to mean
P +1/2 ? v² + ?gh = Constant
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.

11. Kepler'S third law (T and R)
T^2 = k R^3 - k=constant
Dp/dt = L / (t ?V)
Z_c = -i/(?C) ; Z_L = i ? L
P1V1 - P2V2 / (? - 1)

12. Partition Function
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Z = ?g_i*exp(-E/kT)
? exp(-e/t)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

13. Adiabatic means
Isentropic
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
C_eq = ?C_i

14. EM: Reactance of Capacitor
X_C = 1/(i?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
DW/dq
µ=s^2

15. Mech: Impulse
J = ? Fdt
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F = R/2

16. EM: Bremsstrahlung (translation)
Cv = dE/dT = 3R
Braking Radiation
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

17. Mean electron drift speed
Braking Radiation
Ct²-x²-y²-z²
J/(ne) n: atom density
X_L = X_C or X_total = 0

18. Solid: Resistivity of Metal
?~T
Exponentially decreasing radial function
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
DS = 0 - dQ = 0 - P V^? = constant

19. Stark Effect
<T> = 1/2 * <dV/dx>
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
1/vLC
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

20. Center of Mass: Kinetic Energy & Angular Momentum
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
P1V1 - P2V2 / (? - 1)
KE = 1/2 * µ (dr/dt)² L = µ r x v
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

21. Work in a capacitor
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
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.
N d flux / dt
1/2 CV²

22. Bernoulli Equation
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Q = CVexp(-t/RC)
P +1/2 ? v² + ?gh = Constant
V = V0 + V0 a ?T

23. Mech: Virial Theorem
µ0 I1I2 / (2pd)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Int ( A . dr) = Int ( del x A) dSurface
<T> = -<V>/2

24. Coriolis Force
?_max = b/T
F = -2*m(? x r)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

25. Doppler Shift in Frequency
F_f = µ*F_N
F = f* (c+v_r)/(c+v_s)
? exp(-e/t)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

26. Energy in Inductor
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Ct²-x²-y²-z²
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
.5 LI²

27. Magnetic field due to a segment of wire
Z²/n² (m_red/m_elec)
KE = 1/2 * µ (dr/dt)² L = µ r x v
F = µ0 q v I / 2pr
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

28. Inductance of Solenoid
Int ( A . dr) = Int ( del x A) dSurface
Cos[?] Sin[?] -Sin[?] Cos[?]
V = V0 + V0 a ?T
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

29. Entropy (# of states - and in terms of other thermo quantities)
?? = h/mc * (1-cos(?))
S = k ln[O] ; dS = dQ/T
qvb = mv²/R
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

30. Triplet/singlet states: symmetry and net spin
Braking Radiation
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
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.

31. Planck Radiation Law
Hbar*?³/(p²c³exp(hbar?/t)-1)
DW = P dV
<T> = -<V>/2
? (t-vx/c²)

32. Mech: Parallel Axis Theorem (Moment of Inertia)
I_z = I_x + I_y (think hoop symmetry)
Q = CVexp(-t/RC)
I = I_cm + md²
E²-p²c²

33. Thermo: Average Total Energy
?mv
N²/Z (m_elec/m_red)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
(° of Freedom)kT/2

34. Thin Film Theory: Constructive / Destructive Interference
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Const: 2t = (n +.5)? Destructive 2t = n?
F = f* (c+v_r)/(c+v_s)
Z = ?g_i*exp(-E/kT)

35. Effective Potential
V(r) + L²2/2mr²
Dp/dt = L / (t ?V)
Ct²-x²-y²-z²
C_eq = (? 1/C_i)^-1

36. Radiation (Larmor - and another neat fact)
?~1/T
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
B = µ0 I n
S_mean = s/Sqrt[N]

37. Gibbs Factor
P/A = s T^4
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
F = I L X B
Exp(N(µ-e)/t)

38. Stoke'S Theorem
X_L = X_C or X_total = 0
Int ( A . dr) = Int ( del x A) dSurface
A[B -C] + [A -C]B
P/A = s T^4

39. 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.
C_eq = (? 1/C_i)^-1
Q = CVexp(-t/RC)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

40. Poisson distribution (µ and s)
µ=s^2
1/ne - where n is charge carrier density
dU = 0 ? dS = ?dW/T
Hbar*?³/(p²c³exp(hbar?/t)-1)

41. Weighted average (mean and unc. of mean)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
C_eq = (? 1/C_i)^-1
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
I = Im (sinc²(a)) ; a = pai sin(?) / ?

42. Quant: Expectation Value
E = s/e_0
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
<?|O|?>
Faraday/Lenz: current inducted opposes the changing field

43. Addition of relativistic velocities

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44. QM: de Broglie Wavelength
P +1/2 ? v² + ?gh = Constant
?= h/v(2mE)
F_f = µ*F_N
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

45. EM: SHO (Hooke)
1/2 CV²
I = -(c ?t)^2 + d^2
ma + kx = 0
I = Im (sinc²(a)) ; a = pai sin(?) / ?

46. Selection rules for atomic transitions
ih_barL_z
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
C_eq = ?C_i
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

47. Focal point of mirrror with curvature
µ0 I / 2R
F = R/2
S = k ln[O] ; dS = dQ/T
Exponentially decreasing radial function

48. Force on a wire in magnetic field
F = I L X B
.5 LI²
µ0 I1I2 / (2pd)
DS = 0 - dQ = 0 - P V^? = constant

49. Heat added
V(r) + L²2/2mr²
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
<T> = -<V>/2
NC?T

50. Mech: Force of Friction
F_f = µ*F_N
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
? exp(-e/t)
Measurements close to mean