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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. Adiabatic means
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
1/vLC
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Isentropic

2. Parallel axis theorem
I = I_cm + (1/2)m d^2
A[B -C] + [A -C]B
F_f = µ*F_N
Cv = dE/dT = 3R

3. Mech: Force of Friction
µ=s^2
F = R/2
F_f = µ*F_N
DW = P dV

4. Magnetic Field Through Ring
I = Im (sinc²(a)) ; a = pai sin(?) / ?
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Exponentially decreasing radial function
µ0 I / 2R

5. Effective Potential
Z_c = -i/(?C) ; Z_L = i ? L
E = Z²*E1
DW/dq
V(r) + L²2/2mr²

6. SR: Total Energy of a Particle
P/A = s T^4
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
F = s * T4
Sin(?) = ?/d

7. Bragg'S Law of Reflection
M? = 2dsin(?)
E = <?| H |?>
<T> = 1/2 * <dV/dx>
C = 4pe0 ab/(a-b) = inner and outer radii

8. Astro: p-p Chain
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Infinitely close to equilibrium at all times
F = I L X B
4H + 2e- ? He +2? + 6?

9. Clausius-Clapeyron Equation
Dp/dt = L / (t ?V)
0
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
µ0 I / 2pR

10. Induced EMF of solenoid
N d flux / dt
Const: 2t = (n +.5)? Destructive 2t = n?
4H + 2e- ? He +2? + 6?
U - ts = -tlog(Z)

11. Mech: Impulse
? = h/p
J = ? Fdt
I = V/R exp(-t/RC)
Const: 2t = (n +.5)? Destructive 2t = n?

12. Hamiltonian and Hamilton'S equations
Measurements close to true value
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
S_mean = s/Sqrt[N]
C = 4pe0 ab/(a-b) = inner and outer radii

13. Ohm'S Law w/ current density
Opposing charge induced upon conductor
J = E s - s = Conductivity - E = Electric field
µ = m_e/2
? = h/mv

14. Relativistic length contraction
1/ne - where n is charge carrier density
? = h/mv
?? = h/mc * (1-cos(?))
L = L_0 Sqrt[1-v^2/c^2]

15. Electromotive Force
? = h/p
DW/dq
V(r) + L²2/2mr²
B = µ0 I n

16. Solid: Resistivity of Semi-Conductor
Always Real
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
?~1/T
?s = 0 - ?l = ±1

17. A reversible process stays..
E = <?| H |?>
P +1/2 ? v² + ?gh = Constant
Infinitely close to equilibrium at all times
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

18. Rayleigh criterion
µ=s^2
Cv = dE/dT = 3R
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
? = 1.22? / d

19. EM: Method of Images
DS = 0 - dQ = 0 - P V^? = constant
Opposing charge induced upon conductor
I = I_0 Cos[?]^2
dU = 0 ? dS = ?dW/T

20. Kepler'S Three Laws
? = h/p
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
U = t^2 d/dt (logZ)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

21. Kepler'S third law (T and R)
T^2 = k R^3 - k=constant
µ0 I / 2R
? = h/p
F = f* (c+v_r)/(c+v_s)

22. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Opposing charge induced upon conductor
C = 4pe0 ab/(a-b) = inner and outer radii
<T> = 1/2 * <dV/dx>

23. EM: Lorentz Force
E = Z²*E1
F = qv×B
V = V0 + V0 a ?T
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

24. Gibbs Factor
µ = Current * Area T = µ x B
F = qv×B
Exp(N(µ-e)/t)
Asin(?) = m?

25. De Broigle Wavelength
?= h/v(2mE)
? = h/mv
P/A = s T^4
Braking Radiation

26. Mech: Centripetal Force
Exp(N(µ-e)/t)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
F = mv²/r

27. Springs in series/parallel
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
? = 1.22?/D
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Z = ?g_i*exp(-E/kT)

28. Thermo: Partition Function
Z = ?g_i*exp(-E/kT)
DW/dq
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

29. Mech: Parallel Axis Theorem (Moment of Inertia)
Const: 2t = (n +.5)? Destructive 2t = n?
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Dv = -udm/m - v = v0 + u ln(m0/m)
I = I_cm + md²

30. EM: Electric Field inside of Conductor
0
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
KE = 1/2 * µ (dr/dt)² L = µ r x v

31. EM: AC Resonance
?~1/T
X_L = X_C or X_total = 0
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Braking Radiation

32. Adiabatic processes (dS - dQ - P and V)
Dp/dt = L / (t ?V)
? = 1.22?/D
DS = 0 - dQ = 0 - P V^? = constant
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

33. Atom: Positronium Reduced Mass
µ = m_e/2
µ = Current * Area T = µ x B
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

34. Double Slit: Interference Minimum - Diffraction Minimum
Int ( A . dr) = Int ( del x A) dSurface
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

35. Selection Rules
ds² = (c*dt)² - ?(x_i)²
?s = 0 - ?l = ±1
A[B -C] + [A -C]B
I = I_cm + (1/2)m d^2

36. Lensmaker Equation - Thin Lens
Z²/n² (m_red/m_elec)
H = H_0 + ?H
M? = 2dsin(?)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

37. Relativistic Momentum
1/ne - where n is charge carrier density
?mv
J/(ne) n: atom density
I_z = I_x + I_y (think hoop symmetry)

38. Polarizers - intensity when crossed at ?
E = s/e_0
I = I_0 Cos[?]^2
P +1/2 ? v² + ?gh = Constant
F = R/2

39. Inductance of Solenoid
I = I_cm + (1/2)m d^2
Hbar*?³/(p²c³exp(hbar?/t)-1)
I = I_0 Cos[?]^2
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

40. Thermo: 1st Law
?s = 0 - ?l = ±1
S_mean = s/Sqrt[N]
dQ = dW +dU
?= h/v(2mE)

41. 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)
Isentropic
M? = 2dsin(?)
X_L = i?L

42. Commutator identities ( [B -A C] - [A -B] )
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
U = t^2 d/dt (logZ)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Infinitely close to equilibrium at all times

43. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
C_eq = (? 1/C_i)^-1
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
C = 4pe0 ab/(a-b) = inner and outer radii
<T> = -<V>/2

44. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
T = I?²/2
?mc²
Measurements close to true value

45. Resistance - length - area - rho
I = I_cm + (1/2)m d^2
DS = 0 - dQ = 0 - P V^? = constant
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
? = 1.22? / d

46. Force/length between two wires
P² ~ R³
X_C = 1/(i?C)
W_A < W_I
µ0 I1I2 / (2pd)

47. Thermo: Isothermal
DW/dq
dU = 0 ? dS = ?dW/T
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
ds² = (c*dt)² - ?(x_i)²

48. Quant: Eigenvalue of Hermitian Operator
F = I L X B
.5 LI²
<?|O|?>
Always Real

49. Source-free RC Circuit
DW/dq
?_max = b/T
X_L = X_C or X_total = 0
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

50. Boltzmann / Canonical distribution
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
I = I_cm + md²
DS = 0 - dQ = 0 - P V^? = constant
Dv = -udm/m - v = v0 + u ln(m0/m)