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GRE Physics

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Answer 50 questions in 15 minutes.
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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: Hydrogen Wave Function Type
Always Real
Exponentially decreasing radial function
V = -L di/dt
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

2. Magnetic Field of a long solenoid
? (t-vx/c²)
B = µ0 I n
PdV +dU
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

3. Lab: Accuracy of Measurements
Measurements close to true value
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
? = 1.22? / d

4. Quant: Eigenvalue of Hermitian Operator
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Always Real
Measurements close to true value
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

5. 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
S = k ln[O] ; dS = dQ/T
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

6. Rayleigh'S Criterion
E = <?| H |?>
Sin(?) = ?/d
PdV +dU
C_eq = ?C_i

7. Pauli matrices
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
B = µ0 I n
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
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

8. Mech: Virial Theorem
<?|O|?>
F = f* (c+v_r)/(c+v_s)
Braking Radiation
<T> = -<V>/2

9. Spherical Capacitor Equation
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
C = 4pe0 ab/(a-b) = inner and outer radii
Z²/n² (m_red/m_elec)

10. Perpendicular axis theorem
F = µ0 q v I / 2pr
I_z = I_x + I_y (think hoop symmetry)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
(3/2) n R ?t

11. Kepler'S Three Laws
F = µ0 q v I / 2pr
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
I = I_cm + md²

12. Helmholtz Free Energy
U - ts = -tlog(Z)
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
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Dp/dt = L / (t ?V)

13. Poisson distribution (µ and s)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Braking Radiation
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
µ=s^2

14. Hall Coefficient
F = s * T4
S = k ln[O] ; dS = dQ/T
Hbar*?³/(p²c³exp(hbar?/t)-1)
1/ne - where n is charge carrier density

15. Virial Theorem
?s = 0 - ?l = ±1
<T> = 1/2 * <dV/dx>
F = mv²/r
E²-p²c²

16. Biot-Savart law
dQ = dW +dU
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Opposing charge induced upon conductor
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

17. Stefan-Boltzmann law for blackbodies (power per area and T)
I = I_0 Cos[?]^2
U = t^2 d/dt (logZ)
P/A = s T^4
ma + kx = 0

18. Astro: Kepler'S Third Law
E²-p²c²
P² ~ R³
DS = 0 - dQ = 0 - P V^? = constant
(° of Freedom)kT/2

19. Relativistic Momentum
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 = -L di/dt
S_mean = s/Sqrt[N]
?mv

20. Thermo: Average Total Energy
S = k ln[O] ; dS = dQ/T
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
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
(° of Freedom)kT/2

21. Lagrangian and Lagrange'S equation
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Braking Radiation
L = T - V dL/dq = d/dt dL/dqdot
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

22. Current in resistor in RC circuit
F_f = µ*F_N
I = V/R exp(-t/RC)
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
Cv = dE/dT = 3R

23. Mech: Parallel Axis Theorem (Moment of Inertia)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
(3/2) n R ?t
I = I_cm + md²

24. Triplet/singlet states: symmetry and net spin
?mc²
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
T^2 = k R^3 - k=constant
?? = h/mc * (1-cos(?))

25. SR: Spacetime Interval
Opposing charge induced upon conductor
ds² = (c*dt)² - ?(x_i)²
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
ma + kx = 0

26. Doppler shift for light
v(mean)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
µ0 I1I2 / (2pd)
PdV +dU

27. Mech: Centripetal Force
Exponentially decreasing radial function
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
F = mv²/r
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

28. Solid: Resistivity of Semi-Conductor
Ct²-x²-y²-z²
N²/Z (m_elec/m_red)
Z²/n² (m_red/m_elec)
?~1/T

29. EM: Reactance of Inductor
C_eq = ?C_i
? (t-vx/c²)
DW/dq
X_L = i?L

30. Rotation matrix (2x2)
(° of Freedom)kT/2
?max = 2.898 x 10 -³ / T
Cos[?] Sin[?] -Sin[?] Cos[?]
I = -(c ?t)^2 + d^2

31. Entropy (# of states - and in terms of other thermo quantities)
?max = 2.898 x 10 -³ / T
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
X_L = X_C or X_total = 0
S = k ln[O] ; dS = dQ/T

32. Thermo: 1st Law
Z²/n² (m_red/m_elec)
dQ = dW +dU
L = mr²d?/dt
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

33. Mech: Force of Friction
V = -L di/dt
F_f = µ*F_N
?mc²
Cos[?] Sin[?] -Sin[?] Cos[?]

34. Force on a wire in magnetic field
µ0 I / 2R
X_C = 1/(i?C)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
F = I L X B

35. Bragg'S Law of Reflection
M? = 2dsin(?)
X_C = 1/(i?C)
NC?T
DW = P dV

36. Focal point of mirrror with curvature
H = H_0 + ?H
F = R/2
Const: 2t = (n +.5)? Destructive 2t = n?
W_A < W_I

37. Perturbations
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
U - ts = -tlog(Z)
?~1/T
H = H_0 + ?H

38. Magnetic field due to a segment of wire
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
C_eq = ?C_i
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
dU = 0 ? dS = ?dW/T

39. Radiation (Larmor - and another neat fact)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
DW = P dV

40. Induced EMF of solenoid
E = <?| H |?>
N d flux / dt
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
<T> = 1/2 * <dV/dx>

41. Thermo: Isothermal
DS = 0 - dQ = 0 - P V^? = constant
dU = 0 ? dS = ?dW/T
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
?_max = b/T

42. Force exerted on charge by long wire
?~T
F = µ0 q v I / 2pr
F = qv×B
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

43. Parallel axis theorem
I = I_cm + (1/2)m d^2
T = I?²/2
DS = 0 - dQ = 0 - P V^? = constant
Opposing charge induced upon conductor

44. Selection Rules
L = L_0 Sqrt[1-v^2/c^2]
?s = 0 - ?l = ±1
I ' = I cos²(?)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

45. Source Free RL Circuit
KE = 1/2 * µ (dr/dt)² L = µ r x v
C = 4pe0 ab/(a-b) = inner and outer radii
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Hbar*?³/(p²c³exp(hbar?/t)-1)

46. EM: Bremsstrahlung (translation)
Braking Radiation
P/A = s T^4
Hbar*?³/(p²c³exp(hbar?/t)-1)
KE = 1/2 * µ (dr/dt)² L = µ r x v

47. Inductance of Solenoid
C = 4pe0 ab/(a-b) = inner and outer radii
F = R/2
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

48. Doppler Shift in Frequency
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
F = f* (c+v_r)/(c+v_s)
F = µ0 q v I / 2pr
Z_c = -i/(?C) ; Z_L = i ? L

49. Angular momentum - Central Force Motion
L = mr²d?/dt
P +1/2 ? v² + ?gh = Constant
µ=s^2
Dp/dt = L / (t ?V)

50. Mean electron drift speed
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
? exp(-e/t)
J/(ne) n: atom density

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