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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. Biot-Savart law
<T> = -<V>/2
? = 1.22?/D
Sin(?) = ?/d
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

2. Rocket Thrust
KE = 1/2 * µ (dr/dt)² L = µ r x v
u dm/dt
?mv
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

3. Spherical Capacitor Equation
C = 4pe0 ab/(a-b) = inner and outer radii
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
(° of Freedom)kT/2

4. Coriolis Force
?? = h/mc * (1-cos(?))
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
F = -2*m(? x r)

5. Thermo: Isothermal
dU = 0 ? dS = ?dW/T
Asin(?) = m?
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

6. Thin Film Theory: Constructive / Destructive Interference
Const: 2t = (n +.5)? Destructive 2t = n?
P/A = s T^4
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
? = 1.22? / d

7. Resistance - length - area - rho
U = t^2 d/dt (logZ)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

8. Ohm'S Law w/ current density
X_C = 1/(i?C)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
N d flux / dt
J = E s - s = Conductivity - E = Electric field

9. EM: Lorentz Force
ih_barL_z
u dm/dt
F = qv×B
Infinitely close to equilibrium at all times

10. Astro: Aperture Formula (Rayleigh Criterion)
Ct²-x²-y²-z²
I = Im (sinc²(a)) ; a = pai sin(?) / ?
? = 1.22?/D
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

11. Mech: Centripetal Force
Const: 2t = (n +.5)? Destructive 2t = n?
F = 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)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

12. Selection rules for atomic transitions
P² ~ R³
µ = m_e/2
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

13. Source Free RL Circuit
? (t-vx/c²)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
0
u dm/dt

14. Complex impedance (expressions for capacitor and inductor)
V(r) + L²2/2mr²
L = mr²d?/dt
W_A < W_I
Z_c = -i/(?C) ; Z_L = i ? L

15. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Measurements close to true value
(° of Freedom)kT/2
PdV +dU

16. Bernoulli Equation
?? = h/mc * (1-cos(?))
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
1/2 CV²
P +1/2 ? v² + ?gh = Constant

17. Solid: Resistivity of Metal
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
<T> = -<V>/2
?~T
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

18. Radiation (Larmor - and another neat fact)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Faraday/Lenz: current inducted opposes the changing field
Cv = dE/dT = 3R

19. Rayleigh criterion
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.
ds² = (c*dt)² - ?(x_i)²
? = 1.22? / d
I = I_cm + (1/2)m d^2

20. Quant: Orthogonality of States
<?1|?2> = 0 ? Orthogonal
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
ma + kx = 0
Sin(?) = ?/d

21. Stefan-Boltzmann law for blackbodies (power per area and T)
P/A = s T^4
µ=s^2
U = t^2 d/dt (logZ)
V(r) + L²2/2mr²

22. Astro: Kepler'S Third Law
? = 1.22?/D
P² ~ R³
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
H = H_0 + ?H

23. Wein'S displacement law for blackbodies (? and T)
Measurements close to true value
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
?_max = b/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.

24. Quant: Expectation Value
?= h/v(2mE)
Ct²-x²-y²-z²
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
<?|O|?>

25. Magnetic Field For Current in Long Wire
Braking Radiation
µ0 I / 2pR
B = µ0 I n
F = I L X B

26. SR: Total Energy of a Particle
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Exp(N(µ-e)/t)
H = H_0 + ?H

27. Thermo: Partition Function
Z = ?g_i*exp(-E/kT)
F = qv×B
ma + kx = 0
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

28. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Opposing charge induced upon conductor
I = V/R exp(-t/RC)
<?1|?2> = 0 ? Orthogonal

29. Time Lorentz Transformation
0
Z = ?g_i*exp(-E/kT)
? (t-vx/c²)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

30. Work in a capacitor
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
ds² = (c*dt)² - ?(x_i)²
1/2 CV²
qvb = mv²/R

31. Quant: Commutator Relation [AB -C]
ih_barL_z
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
A[B -C] + [A -C]B
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

32. Virial Theorem
I = I_cm + md²
L = L_0 Sqrt[1-v^2/c^2]
<T> = 1/2 * <dV/dx>
Int ( A . dr) = Int ( del x A) dSurface

33. Work done on a gas
DW = P dV
Braking Radiation
I ' = I cos²(?)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

34. Center of Mass: Kinetic Energy & Angular Momentum
KE = 1/2 * µ (dr/dt)² L = µ r x v
V(r) + L²2/2mr²
P/A = s T^4
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

35. Force on a wire in magnetic field
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
U - ts = -tlog(Z)
M? = 2dsin(?)
F = I L X B

36. Energy levels from the Coulomb potential
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

37. Rayleigh'S Criterion
S_mean = s/Sqrt[N]
P/A = s T^4
Sin(?) = ?/d
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

38. Atom: Bohr Formula
B = µ0 I n
S_mean = s/Sqrt[N]
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
N d flux / dt

39. Partition Function
? exp(-e/t)
1/2 CV²
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
B = µ0 I n

40. td(entropy) =
PdV +dU
µ = Current * Area T = µ x B
DS = 0 - dQ = 0 - P V^? = constant
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

41. Mech: Parallel Axis Theorem (Moment of Inertia)
V = -L di/dt
I = I_cm + md²
C = 4pe0 ab/(a-b) = inner and outer radii
?mv

42. Bohr Model: Radii
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.
?max = 2.898 x 10 -³ / T
DW = P dV
N²/Z (m_elec/m_red)

43. Bohr Model: Energy
?~1/T
C_eq = (? 1/C_i)^-1
Z²/n² (m_red/m_elec)
P1V1 - P2V2 / (? - 1)

44. Internal Energy of an Ideal Gas
N²/Z (m_elec/m_red)
1/ne - where n is charge carrier density
µ0 I1I2 / (2pd)
(3/2) n R ?t

45. Clausius-Clapeyron Equation
H = H_0 + ?H
Exp(N(µ-e)/t)
F = s * T4
Dp/dt = L / (t ?V)

46. Lab: Accuracy of Measurements
Ct²-x²-y²-z²
L = mr²d?/dt
E²-p²c²
Measurements close to true value

47. Electromotive Force
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Dp/dt = L / (t ?V)
I = V/R exp(-t/RC)
DW/dq

48. Thermo: Adiabatic Work vs Isothermal Work
W_A < W_I
Z_c = -i/(?C) ; Z_L = i ? L
qvb = mv²/R
L = mr²d?/dt

49. Lab: Precision of Measurements
J = E s - s = Conductivity - E = Electric field
Measurements close to mean
Z²/n² (m_red/m_elec)
Const: 2t = (n +.5)? Destructive 2t = n?

50. Relativistic Energy
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
P1V1 - P2V2 / (? - 1)
T^2 = k R^3 - k=constant
?mc²