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GRE Physics

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Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Inductance of Solenoid
NC?T
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Hbar*?³/(p²c³exp(hbar?/t)-1)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

2. Thermo: Average Total Energy
(° of Freedom)kT/2
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
I = Im (sinc²(a)) ; a = pai sin(?) / ?
? = 1.22?/D

3. Bragg'S Law of Reflection
E = <?| H |?>
M? = 2dsin(?)
P1V1 - P2V2 / (? - 1)
F = µ0 q v I / 2pr

4. Quant: [L_x -L_y] = ?
I = I_cm + md²
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
ih_barL_z
ma + kx = 0

5. Source Free RL Circuit
Measurements close to true value
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
E = s/e_0
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

6. Hall Coefficient
1/ne - where n is charge carrier density
KE = 1/2 * µ (dr/dt)² L = µ r x v
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
<?1|?2> = 0 ? Orthogonal

7. Electromotive Force
Braking Radiation
I = V/R exp(-t/RC)
DW/dq
Q = CVexp(-t/RC)

8. Work done on a gas
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
L = L_0 Sqrt[1-v^2/c^2]
DW = P dV

9. Thin Film Theory: Constructive / Destructive Interference
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Const: 2t = (n +.5)? Destructive 2t = n?
1/ne - where n is charge carrier density
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

10. Relativistic Energy
.5 LI²
V(r) + L²2/2mr²
NC?T
?mc²

11. td(entropy) =
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
1/vLC
PdV +dU
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

12. Quant: Commutator Relation [AB -C]
P +1/2 ? v² + ?gh = Constant
A[B -C] + [A -C]B
H = H_0 + ?H
Braking Radiation

13. Heat added
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
? = 5/3
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
NC?T

14. Weighted average (mean and unc. of mean)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Int ( A . dr) = Int ( del x A) dSurface
Exponentially decreasing radial function
?_max = b/T

15. Lab: Precision of Measurements
X_L = X_C or X_total = 0
Measurements close to mean
I = Im (sinc²(a)) ; a = pai sin(?) / ?
<T> = -<V>/2

16. Adiabatic processes (dS - dQ - P and V)
? exp(-e/t)
?~1/T
Cv = dE/dT = 3R
DS = 0 - dQ = 0 - P V^? = constant

17. Parallel axis theorem
Always Real
Cv = dE/dT = 3R
?~T
I = I_cm + (1/2)m d^2

18. Double Slit: Interference Minimum - Diffraction Minimum
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
I = I_cm + (1/2)m d^2
µ = Current * Area T = µ x B
H = H_0 + ?H

19. Focal point of mirrror with curvature
F = R/2
µ = Current * Area T = µ x B
Always Real
KE = 1/2 * µ (dr/dt)² L = µ r x v

20. A reversible process stays..
U = t^2 d/dt (logZ)
Infinitely close to equilibrium at all times
P² ~ R³
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

21. Compton Scattering
E = s/e_0
?? = h/mc * (1-cos(?))
U = t^2 d/dt (logZ)
P/A = s T^4

22. Mech: Virial Theorem
µ0 I / 2pR
<T> = -<V>/2
? = 1.22?/D
<?1|?2> = 0 ? Orthogonal

23. Force on a wire in magnetic field
?_max = b/T
F = I L X B
F_f = µ*F_N
(° of Freedom)kT/2

24. Energy levels from the Coulomb potential
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
<?1|?2> = 0 ? Orthogonal
U - ts = -tlog(Z)
E = s/e_0

25. Atom: Bohr Formula
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
V = -L di/dt
<?1|?2> = 0 ? Orthogonal
µ0 I / 2R

26. Gibbs Factor
X_L = i?L
Exp(N(µ-e)/t)
µ0 I1I2 / (2pd)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

27. Magnetic field due to a segment of wire
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
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.
E = s/e_0
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

28. EM: Parallel Capacitance
Cv = dE/dT = 3R
F = -2*m(? x r)
C_eq = ?C_i
Dp/dt = L / (t ?V)

29. Angular momentum - Central Force Motion
?? = h/mc * (1-cos(?))
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
?~T
L = mr²d?/dt

30. Magnetic Dipole Moment and Torque
U - ts = -tlog(Z)
µ = Current * Area T = µ x B
<?|O|?>
S_mean = s/Sqrt[N]

31. Biot-Savart law
PdV +dU
W_A < W_I
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^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.

32. Relativistic Momentum
Measurements close to mean
?mv
µ = Current * Area T = µ x B
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

33. Force exerted on charge by long wire
S = k ln[O] ; dS = dQ/T
F = s * T4
F = µ0 q v I / 2pr
C_eq = ?C_i

34. Mech: Impulse
J = ? Fdt
dQ = dW +dU
Infinitely close to equilibrium at all times
1/vLC

35. Thermo: Partition Function
E = Z²*E1
0
<?|O|?>
Z = ?g_i*exp(-E/kT)

36. Ohm'S Law w/ current density
Exponentially decreasing radial function
B = µ0 I n
U = t^2 d/dt (logZ)
J = E s - s = Conductivity - E = Electric field

37. Mech: Parallel Axis Theorem (Moment of Inertia)
0
I = I_cm + md²
S = k ln[O] ; dS = dQ/T
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

38. E field of a capacitor (d->0)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
J = ? Fdt
E = s/e_0
?~1/T

39. Work in a capacitor
Cos[?] Sin[?] -Sin[?] Cos[?]
P1V1 - P2V2 / (? - 1)
1/2 CV²
T = I?²/2

40. Kepler'S third law (T and R)
.5 LI²
T^2 = k R^3 - k=constant
dQ = dW +dU
1/ne - where n is charge carrier density

41. Thermo: Blackbody Radiation
F = s * T4
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
E = s/e_0
L = T - V dL/dq = d/dt dL/dqdot

42. Solid: Resistivity of Metal
?~T
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
? = h/p
E = Z²*E1

43. Lab: Standard Deviation of Poisson
H = H_0 + ?H
<T> = 1/2 * <dV/dx>
v(mean)
? exp(-e/t)

44. Relativistic interval (which must remain constant for two events)
?~1/T
X_C = 1/(i?C)
C_eq = ?C_i
I = -(c ?t)^2 + d^2

45. Bohr Model: Energy
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Z²/n² (m_red/m_elec)
I = I_cm + md²
Cos[?] Sin[?] -Sin[?] Cos[?]

46. Astro: Kepler'S Third Law
?mv
Asin(?) = m?
P² ~ R³
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

47. Self Inductance
F = mv²/r
V = -L di/dt
I = Im (sinc²(a)) ; a = pai sin(?) / ?
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.

48. Hamiltonian and Hamilton'S equations
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
µ = Current * Area T = µ x B
I ' = I cos²(?)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

49. Wein'S displacement law for blackbodies (? and T)
Infinitely close to equilibrium at all times
?_max = b/T
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
E = s/e_0

50. Atom: Bohr Theory Ionization
N²/Z (m_elec/m_red)
? = h/mv
E = Z²*E1
1/ne - where n is charge carrier density

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