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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. SR: Total Energy of a Particle
qvb = mv²/R
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
u dm/dt

2. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
1/ne - where n is charge carrier density

3. Thermo: Blackbody Radiation
(° of Freedom)kT/2
J/(ne) n: atom density
F = s * T4
DW = P dV

4. Work done on a gas
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
U = t^2 d/dt (logZ)
DW = P dV

5. Perturbations
?~T
C = 4pe0 ab/(a-b) = inner and outer radii
H = H_0 + ?H
P +1/2 ? v² + ?gh = Constant

6. Entropy (# of states - and in terms of other thermo quantities)
Asin(?) = m?
4H + 2e- ? He +2? + 6?
S = k ln[O] ; dS = dQ/T
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

7. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
I = I_cm + md²
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Ct²-x²-y²-z²
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

8. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Braking Radiation
Z_c = -i/(?C) ; Z_L = i ? L
P +1/2 ? v² + ?gh = Constant

9. Magnetic field due to a segment of wire
S = k ln[O] ; dS = dQ/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
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
V = V0 + V0 a ?T

10. Stark Effect
Dv = -udm/m - v = v0 + u ln(m0/m)
Ct²-x²-y²-z²
P1V1 - P2V2 / (? - 1)
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

11. Adiabatic means
P +1/2 ? v² + ?gh = Constant
Isentropic
? = 5/3
I = I_0 Cos[?]^2

12. Selection Rules
?s = 0 - ?l = ±1
dQ = dW +dU
S_mean = s/Sqrt[N]
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

13. Effective Potential
V(r) + L²2/2mr²
ih_barL_z
Opposing charge induced upon conductor
A[B -C] + [A -C]B

14. Kepler'S third law (T and R)
T^2 = k R^3 - k=constant
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Hbar*?³/(p²c³exp(hbar?/t)-1)
u dm/dt

15. EM: Maxwell'S equations
dU = 0 ? dS = ?dW/T
?mv
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Z = ?g_i*exp(-E/kT)

16. QM: de Broglie Wavelength
L = T - V dL/dq = d/dt dL/dqdot
?= h/v(2mE)
<?1|?2> = 0 ? Orthogonal
(° of Freedom)kT/2

17. Mech: Force of Friction
Cos[?] Sin[?] -Sin[?] Cos[?]
I = I_0 Cos[?]^2
F_f = µ*F_N
V = V0 + V0 a ?T

18. Rotation matrix (2x2)
ds² = (c*dt)² - ?(x_i)²
Cos[?] Sin[?] -Sin[?] Cos[?]
? = h/mv
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

19. Coriolis Force
F = -2*m(? x r)
S_mean = s/Sqrt[N]
dQ = dW +dU
Ct²-x²-y²-z²

20. Dulong Petit Law
S_mean = s/Sqrt[N]
Asin(?) = m?
Cv = dE/dT = 3R
F_f = µ*F_N

21. Lagrangian and Lagrange'S equation
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
X_L = X_C or X_total = 0
L = T - V dL/dq = d/dt dL/dqdot
I = I_0 Cos[?]^2

22. Bohr Model: Radii
N²/Z (m_elec/m_red)
Always Real
µ0 I1I2 / (2pd)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

23. Bernoulli Equation
E = <?| H |?>
C_eq = (? 1/C_i)^-1
P +1/2 ? v² + ?gh = Constant
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

24. EM: Reactance of Inductor
X_L = X_C or X_total = 0
Dp/dt = L / (t ?V)
X_L = i?L
?? = h/mc * (1-cos(?))

25. Rayleigh'S Criterion
v(mean)
I = -(c ?t)^2 + d^2
Sin(?) = ?/d
F = R/2

26. Adiabatic processes (dS - dQ - P and V)
ma + kx = 0
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
DS = 0 - dQ = 0 - P V^? = constant
1/ne - where n is charge carrier density

27. Force exerted on charge by long wire
?? = h/mc * (1-cos(?))
F = µ0 q v I / 2pr
? (t-vx/c²)
Q = CVexp(-t/RC)

28. De Broigle Wavelength
H = H_0 + ?H
A[B -C] + [A -C]B
T = I?²/2
? = h/mv

29. Atom: Bohr Theory Ionization
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
C_eq = (? 1/C_i)^-1
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
E = Z²*E1

30. Wein'S Displacement Law
Asin(?) = m?
?max = 2.898 x 10 -³ / T
4H + 2e- ? He +2? + 6?
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

31. Angular momentum operators L^2 and L_z
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.
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Const: 2t = (n +.5)? Destructive 2t = n?
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

32. Current in resistor in RC circuit
Dv = -udm/m - v = v0 + u ln(m0/m)
I = V/R exp(-t/RC)
W_A < W_I
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

33. Center of Mass: Kinetic Energy & Angular Momentum
J = E s - s = Conductivity - E = Electric field
Always Real
KE = 1/2 * µ (dr/dt)² L = µ r x v
µ0 I / 2R

34. A reversible process stays..
I = V/R exp(-t/RC)
L = T - V dL/dq = d/dt dL/dqdot
Infinitely close to equilibrium at all times
Int ( A . dr) = Int ( del x A) dSurface

35. Atom: Bohr Formula
Opposing charge induced upon conductor
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
H = H_0 + ?H
J = ? Fdt

36. Lensmaker Equation - Thin Lens
Exp(N(µ-e)/t)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
dQ = dW +dU

37. Internal Energy of an Ideal Gas
(3/2) n R ?t
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.
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
V = -L di/dt

38. Ohm'S Law w/ current density
? exp(-e/t)
J = E s - s = Conductivity - E = Electric field
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

39. Focal point of mirrror with curvature
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
X_C = 1/(i?C)
? (t-vx/c²)
F = R/2

40. Solid: Resistivity of Metal
Sin(?) = ?/d
Cos[?] Sin[?] -Sin[?] Cos[?]
<T> = 1/2 * <dV/dx>
?~T

41. Lab: Standard Deviation of Poisson
?_max = b/T
I = V/R exp(-t/RC)
DS = 0 - dQ = 0 - P V^? = constant
v(mean)

42. Magnetic Field of a long solenoid
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
µ = m_e/2
B = µ0 I n

43. EM: Series Capacitance
Exponentially decreasing radial function
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Hbar*?³/(p²c³exp(hbar?/t)-1)
C_eq = (? 1/C_i)^-1

44. Quant: Commutator Relation [AB -C]
?~T
u dm/dt
A[B -C] + [A -C]B
ds² = (c*dt)² - ?(x_i)²

45. Double Slit: Interference Minimum - Diffraction Minimum
NC?T
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
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.

46. Addition of relativistic velocities

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47. Lab: Accuracy of Measurements
V(r) + L²2/2mr²
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
P1V1 - P2V2 / (? - 1)
Measurements close to true value

48. td(entropy) =
Ct²-x²-y²-z²
PdV +dU
P² ~ R³
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

49. EM: Electromagnetic inertia
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Faraday/Lenz: current inducted opposes the changing field
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
F = mv²/r

50. Single Slit Diffraction Maximum
1/2 CV²
?max = 2.898 x 10 -³ / T
?= h/v(2mE)
Asin(?) = m?