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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. Thermo: Blackbody Radiation
F = s * T4
F = mv²/r
Infinitely close to equilibrium at all times
v(mean)

2. Work in a capacitor
M? = 2dsin(?)
N d flux / dt
1/2 CV²
v(mean)

3. Magnetic Field of a long solenoid
B = µ0 I n
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
? = 1.22? / d

4. Quant: [L_x -L_y] = ?
ds² = (c*dt)² - ?(x_i)²
J = ? Fdt
F = -2*m(? x r)
ih_barL_z

5. QM: de Broglie Wavelength
dU = 0 ? dS = ?dW/T
X_C = 1/(i?C)
?= h/v(2mE)
Infinitely close to equilibrium at all times

6. Delta Function Potential - type of WF
DS = 0 - dQ = 0 - P V^? = constant
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
I = V/R exp(-t/RC)
1/2 CV²

7. EM: Bremsstrahlung (translation)
Braking Radiation
Exponentially decreasing radial function
T = I?²/2
Dv = -udm/m - v = v0 + u ln(m0/m)

8. Relativistic interval (which must remain constant for two events)
I = -(c ?t)^2 + d^2
NC?T
Cos[?] Sin[?] -Sin[?] Cos[?]
Dv = -udm/m - v = v0 + u ln(m0/m)

9. Thermo: 1st Law
<T> = -<V>/2
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
? exp(-e/t)
dQ = dW +dU

10. Energy in a Capacitor
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
.5 CV²
?max = 2.898 x 10 -³ / T
I = I_0 Cos[?]^2

11. Work done on a gas
F = µ0 q v I / 2pr
DW = P dV
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
(° of Freedom)kT/2

12. Angular momentum operators L^2 and L_z
ds² = (c*dt)² - ?(x_i)²
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
<T> = -<V>/2

13. Lab: Accuracy of Measurements
? = h/mv
V(r) + L²2/2mr²
Measurements close to true value
ma + kx = 0

14. Atom: Hydrogen Wave Function Type
Z²/n² (m_red/m_elec)
? = ?0 root((1-v/c)/(1+v/c))
DW = P dV
Exponentially decreasing radial function

15. Rocket Equation
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
S_mean = s/Sqrt[N]
Dv = -udm/m - v = v0 + u ln(m0/m)
? exp(-e/t)

16. How to derive cylcotron frequency
Const: 2t = (n +.5)? Destructive 2t = n?
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.
qvb = mv²/R
N d flux / dt

17. Magnetic Dipole Moment and Torque
µ = Current * Area T = µ x B
L = mr²d?/dt
L = T - V dL/dq = d/dt dL/dqdot
P/A = s T^4

18. Kepler'S Three Laws
I = -(c ?t)^2 + d^2
dQ = dW +dU
Sin(?) = ?/d
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

19. Mech: Impulse
J = ? Fdt
E²-p²c²
NC?T
I = V/R exp(-t/RC)

20. EM: Electric Field inside of Conductor
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
0
T^2 = k R^3 - k=constant
Dp/dt = L / (t ?V)

21. Selection Rules
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Opposing charge induced upon conductor
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?s = 0 - ?l = ±1

22. Double Slit: Interference Minimum - Diffraction Minimum
F = s * T4
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
0
Braking Radiation

23. Magnetic Field Through Ring
µ0 I / 2R
M? = 2dsin(?)
µ = m_e/2
B = µ0 I n

24. Energy in Inductor
C_eq = ?C_i
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
.5 LI²

25. Rayleigh criterion
ma + kx = 0
U - ts = -tlog(Z)
µ0 I1I2 / (2pd)
? = 1.22? / d

26. Invariant spatial quantity
Opposing charge induced upon conductor
Ct²-x²-y²-z²
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
v(mean)

27. Adiabatic processes (dS - dQ - P and V)
I = I_0 Cos[?]^2
DS = 0 - dQ = 0 - P V^? = constant
? = 5/3
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

28. Quant: Eigenvalue of Hermitian Operator
?mc²
N²/Z (m_elec/m_red)
? (t-vx/c²)
Always Real

29. Complex impedance (expressions for capacitor and inductor)
Z_c = -i/(?C) ; Z_L = i ? L
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
T = I?²/2

30. Lab: Precision of Measurements
µ = Current * Area T = µ x B
Measurements close to mean
J/(ne) n: atom density
Int ( A . dr) = Int ( del x A) dSurface

31. Thermo: Partition Function
? exp(-e/t)
Z = ?g_i*exp(-E/kT)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
u dm/dt

32. Induced EMF of solenoid
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
N d flux / dt
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

33. Rayleigh'S Criterion
Sin(?) = ?/d
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
L = T - V dL/dq = d/dt dL/dqdot
E = Z²*E1

34. Force/length between two wires
1/vLC
µ0 I1I2 / (2pd)
ds² = (c*dt)² - ?(x_i)²
?? = h/mc * (1-cos(?))

35. Effective Potential
ds² = (c*dt)² - ?(x_i)²
I = V/R exp(-t/RC)
u dm/dt
V(r) + L²2/2mr²

36. EM: Maxwell'S equations
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
.5 CV²
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

37. EM: Reactance of Capacitor
J = E s - s = Conductivity - E = Electric field
Z = ?g_i*exp(-E/kT)
X_C = 1/(i?C)
0

38. Resistance - length - area - rho
? = h/p
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
V = -L di/dt
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

39. EM: SHO (Hooke)
I_z = I_x + I_y (think hoop symmetry)
E = Z²*E1
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
ma + kx = 0

40. Bohr Model: Energy
Exp(N(µ-e)/t)
Z²/n² (m_red/m_elec)
F = qv×B
? exp(-e/t)

41. Adiabatic means
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>
Isentropic
M? = 2dsin(?)

42. Helmholtz Free Energy
U - ts = -tlog(Z)
B = µ0 I n
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
.5 CV²

43. Atom: Orbital Config
Const: 2t = (n +.5)? Destructive 2t = n?
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
L = L_0 Sqrt[1-v^2/c^2]
dU = 0 ? dS = ?dW/T

44. Rotation matrix (2x2)
Faraday/Lenz: current inducted opposes the changing field
Cos[?] Sin[?] -Sin[?] Cos[?]
?s = 0 - ?l = ±1
L = mr²d?/dt

45. EM: Reactance of Inductor
X_L = i?L
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
L = T - V dL/dq = d/dt dL/dqdot
E = <?| H |?>

46. Bragg'S Law of Reflection
M? = 2dsin(?)
(3/2) n R ?t
C_eq = (? 1/C_i)^-1
P/A = s T^4

47. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
E = <?| 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

48. Rocket Thrust
u dm/dt
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
E²-p²c²
µ0 I / 2pR

49. Single Slit Diffraction Intensity
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.
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
L = mr²d?/dt
I = Im (sinc²(a)) ; a = pai sin(?) / ?

50. E field of a capacitor (d->0)
KE = 1/2 * µ (dr/dt)² L = µ r x v
? = 1.22? / d
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
E = s/e_0