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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. td(entropy) =
? (t-vx/c²)
PdV +dU
Exp(N(µ-e)/t)
(° of Freedom)kT/2

2. Work done on a gas
DW = P dV
Exp(N(µ-e)/t)
V = V0 + V0 a ?T
Z_c = -i/(?C) ; Z_L = i ? L

3. EM: Parallel Capacitance
? = 1.22? / d
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
C_eq = ?C_i
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

4. Magnetic Field of a long solenoid
B = µ0 I n
Asin(?) = m?
µ = m_e/2
I = Im (sinc²(a)) ; a = pai sin(?) / ?

5. Focal point of mirrror with curvature
µ = Current * Area T = µ x B
F = R/2
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
0

6. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
u dm/dt
? = ?0 root((1-v/c)/(1+v/c))
Braking Radiation

7. Lab: Precision of Measurements
Measurements close to mean
F = I L X B
µ=s^2
? = h/mv

8. Compton Scattering
I = I_0 Cos[?]^2
? = 1.22?/D
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
?? = h/mc * (1-cos(?))

9. Self Inductance
C_eq = (? 1/C_i)^-1
E = Z²*E1
V = -L di/dt
dQ = dW +dU

10. Virial Theorem
<T> = 1/2 * <dV/dx>
C_eq = ?C_i
F = qv×B
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

11. Atom: Positronium Reduced Mass
µ = m_e/2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
H = H_0 + ?H
J/(ne) n: atom density

12. Rocket Thrust
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
u dm/dt
? = h/mv
Cos[?] Sin[?] -Sin[?] Cos[?]

13. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
qvb = mv²/R
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
µ0 I / 2pR

14. Force/length between two wires
P/A = s T^4
? = 1.22?/D
µ0 I1I2 / (2pd)
Exponentially decreasing radial function

15. Perpendicular axis theorem
Hbar*?³/(p²c³exp(hbar?/t)-1)
? (t-vx/c²)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
I_z = I_x + I_y (think hoop symmetry)

16. Atom: Orbital Config
E²-p²c²
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
J = E s - s = Conductivity - E = Electric field
Infinitely close to equilibrium at all times

17. Clausius-Clapeyron Equation
L = T - V dL/dq = d/dt dL/dqdot
Dp/dt = L / (t ?V)
C_eq = (? 1/C_i)^-1
u dm/dt

18. Force on a wire in magnetic field
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
(3/2) n R ?t
1/2 CV²
F = I L X B

19. Mech: Impulse
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
µ0 I1I2 / (2pd)
J = ? Fdt
A[B -C] + [A -C]B

20. Complex impedance (expressions for capacitor and inductor)
C = 4pe0 ab/(a-b) = inner and outer radii
Measurements close to mean
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Z_c = -i/(?C) ; Z_L = i ? L

21. Thermo: Blackbody Radiation
I = Im (sinc²(a)) ; a = pai sin(?) / ?
F = s * T4
µ0 I / 2pR
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

22. Thin Film Theory: Constructive / Destructive Interference
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
L = T - V dL/dq = d/dt dL/dqdot
Const: 2t = (n +.5)? Destructive 2t = n?
Always Real

23. EM: SHO (Hooke)
X_C = 1/(i?C)
ma + kx = 0
S_mean = s/Sqrt[N]
P/A = s T^4

24. Bohr Model: Energy
u dm/dt
F = f* (c+v_r)/(c+v_s)
Z²/n² (m_red/m_elec)
PdV +dU

25. Doppler Shift in Frequency
(° of Freedom)kT/2
F = f* (c+v_r)/(c+v_s)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
?_max = b/T

26. Astro: p-p Chain
<?1|?2> = 0 ? Orthogonal
C = 4pe0 ab/(a-b) = inner and outer radii
4H + 2e- ? He +2? + 6?
V(r) + L²2/2mr²

27. E field of a capacitor (d->0)
dU = 0 ? dS = ?dW/T
F = I L X B
E = s/e_0
P² ~ R³

28. Single Slit Diffraction Intensity
N d flux / dt
V = -L di/dt
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

29. Entropy (# of states - and in terms of other thermo quantities)
S = k ln[O] ; dS = dQ/T
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
1/2 CV²
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

30. Quant: Orthogonality of States
? = 1.22?/D
<?1|?2> = 0 ? Orthogonal
T = I?²/2
Dp/dt = L / (t ?V)

31. Resistance - length - area - rho
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
µ=s^2
L = T - V dL/dq = d/dt dL/dqdot
C_eq = (? 1/C_i)^-1

32. EM: Bremsstrahlung (translation)
? exp(-e/t)
U = t^2 d/dt (logZ)
C = 4pe0 ab/(a-b) = inner and outer radii
Braking Radiation

33. Helmholtz Free Energy
µ = Current * Area T = µ x B
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
U - ts = -tlog(Z)
Exponentially decreasing radial function

34. RLC resonance condition
.5 LI²
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Const: 2t = (n +.5)? Destructive 2t = n?
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

35. First law of thermodynamics (explain direction of energy for each term)
?_max = b/T
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
DW = P dV

36. Polarizers - intensity when crossed at ?
<?|O|?>
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Exponentially decreasing radial function
I = I_0 Cos[?]^2

37. Energy in Inductor
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
.5 LI²
1/ne - where n is charge carrier density
L = mr²d?/dt

38. Anomalous Zeeman Effect

39. Charge in Capacitor
Q = CVexp(-t/RC)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
N d flux / dt
Int ( A . dr) = Int ( del x A) dSurface

40. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
? = h/mv
<T> = -<V>/2
?mc²

41. Rocket Equation
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Dv = -udm/m - v = v0 + u ln(m0/m)
4H + 2e- ? He +2? + 6?
Dp/dt = L / (t ?V)

42. Electromotive Force
T = I?²/2
DW/dq
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
? (t-vx/c²)

43. Expectation value of the energy of state |?>
E = <?| H |?>
<T> = 1/2 * <dV/dx>
Int ( A . dr) = Int ( del x A) dSurface
? (t-vx/c²)

44. Springs in series/parallel
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Cos[?] Sin[?] -Sin[?] Cos[?]
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
X_L = X_C or X_total = 0

45. EM: Lorentz Force
?~1/T
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
F = qv×B
<T> = 1/2 * <dV/dx>

46. Error in the mean if each measurement has the same uncertainty s
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
<T> = 1/2 * <dV/dx>
S_mean = s/Sqrt[N]
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

47. Bragg'S Law of Reflection
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Opposing charge induced upon conductor
?_max = b/T
M? = 2dsin(?)

48. Planck Radiation Law
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Hbar*?³/(p²c³exp(hbar?/t)-1)
I = V/R exp(-t/RC)

49. Bernoulli Equation
DW/dq
Hbar*?³/(p²c³exp(hbar?/t)-1)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
P +1/2 ? v² + ?gh = Constant

50. How to derive cylcotron frequency
? = ?0 root((1-v/c)/(1+v/c))
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
L = L_0 Sqrt[1-v^2/c^2]
qvb = mv²/R