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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. Energy in Inductor
ds² = (c*dt)² - ?(x_i)²
.5 LI²
µ0 I / 2R
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

2. Stoke'S Theorem
Int ( A . dr) = Int ( del x A) dSurface
? = 1.22?/D
F = f* (c+v_r)/(c+v_s)
Faraday/Lenz: current inducted opposes the changing field

3. Work in a capacitor
Faraday/Lenz: current inducted opposes the changing field
dU = 0 ? dS = ?dW/T
1/2 CV²
ds² = (c*dt)² - ?(x_i)²

4. EM: Bremsstrahlung (translation)
F = mv²/r
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
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Braking Radiation

5. Spherical Capacitor Equation
W_A < W_I
C = 4pe0 ab/(a-b) = inner and outer radii
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Int ( A . dr) = Int ( del x A) dSurface

6. Thermo: Partition Function
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
? = h/p
Z = ?g_i*exp(-E/kT)
L = mr²d?/dt

7. Thermo: Adiabatic Work vs Isothermal Work
Exponentially decreasing radial function
M? = 2dsin(?)
?= h/v(2mE)
W_A < W_I

8. Mech: Force of Friction
Measurements close to mean
DW/dq
F_f = µ*F_N
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

9. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
F_f = µ*F_N
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
PdV +dU
X_L = X_C or X_total = 0

10. Angular momentum - Central Force Motion
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
? = h/p
L = mr²d?/dt
I_z = I_x + I_y (think hoop symmetry)

11. Astro: p-p Chain
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
4H + 2e- ? He +2? + 6?
Braking Radiation
Hbar*?³/(p²c³exp(hbar?/t)-1)

12. Mech: Parallel Axis Theorem (Moment of Inertia)
S = k ln[O] ; dS = dQ/T
I = I_cm + md²
DW/dq
Q = CVexp(-t/RC)

13. Atom: Hydrogen Wave Function Type
U = t^2 d/dt (logZ)
1/2 CV²
Exponentially decreasing radial function
Cv = dE/dT = 3R

14. Complex impedance (expressions for capacitor and inductor)
? exp(-e/t)
V = -L di/dt
Z_c = -i/(?C) ; Z_L = i ? L
?? = h/mc * (1-cos(?))

15. Induced EMF of solenoid
S = k ln[O] ; dS = dQ/T
? = 1.22?/D
N d flux / dt
µ0 I1I2 / (2pd)

16. EM: Maxwell'S equations
?max = 2.898 x 10 -³ / T
I = Im (sinc²(a)) ; a = pai sin(?) / ?
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

17. Ohm'S Law w/ current density
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Hbar*?³/(p²c³exp(hbar?/t)-1)
J = E s - s = Conductivity - E = Electric field
F = R/2

18. Source Free RL Circuit
dU = 0 ? dS = ?dW/T
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Ct²-x²-y²-z²

19. Selection Rules
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
?s = 0 - ?l = ±1
N d flux / dt
.5 CV²

20. EM: Electric Field inside of Conductor
T = I?²/2
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
0

21. Current in resistor in RC circuit
I = V/R exp(-t/RC)
ds² = (c*dt)² - ?(x_i)²
I_z = I_x + I_y (think hoop symmetry)
µ = Current * Area T = µ x B

22. Thermo: Blackbody Radiation
F = s * T4
ma + kx = 0
M? = 2dsin(?)
1/ne - where n is charge carrier density

23. Rocket Equation
A[B -C] + [A -C]B
(° of Freedom)kT/2
Dv = -udm/m - v = v0 + u ln(m0/m)
0

24. Planck Radiation Law
µ=s^2
Hbar*?³/(p²c³exp(hbar?/t)-1)
F = R/2
1/2 CV²

25. Biot-Savart law
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
F_f = µ*F_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.
U = t^2 d/dt (logZ)

26. Error in the mean if each measurement has the same uncertainty s
µ0 I / 2R
S_mean = s/Sqrt[N]
? = 5/3
1/vLC

27. Force/length between two wires
µ0 I1I2 / (2pd)
C = 4pe0 ab/(a-b) = inner and outer radii
M? = 2dsin(?)
Faraday/Lenz: current inducted opposes the changing field

28. Commutator identities ( [B -A C] - [A -B] )
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
F = µ0 q v I / 2pr
(3/2) n R ?t
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

29. Magnetic Field For Current in Long Wire
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Z²/n² (m_red/m_elec)
F = mv²/r
µ0 I / 2pR

30. Double Slit: Interference Minimum - Diffraction Minimum
4H + 2e- ? He +2? + 6?
I = V/R exp(-t/RC)
E²-p²c²
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

31. First law of thermodynamics (explain direction of energy for each term)
F = qv×B
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Q = CVexp(-t/RC)
? = 1.22?/D

32. Relativistic interval (which must remain constant for two events)
? = 5/3
DS = 0 - dQ = 0 - P V^? = constant
I = -(c ?t)^2 + d^2
.5 CV²

33. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
V = V0 + V0 a ?T
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>

34. Parallel axis theorem
? = 1.22?/D
I = I_cm + (1/2)m d^2
µ=s^2
?_max = b/T

35. Bohr Model: Radii
Q = CVexp(-t/RC)
X_C = 1/(i?C)
?s = 0 - ?l = ±1
N²/Z (m_elec/m_red)

36. EM: Parallel Capacitance
?s = 0 - ?l = ±1
Infinitely close to equilibrium at all times
C_eq = ?C_i
dU = 0 ? dS = ?dW/T

37. Lensmaker Equation - Thin Lens
X_C = 1/(i?C)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

38. Volumetric Expansion
W_A < W_I
I = V/R exp(-t/RC)
V = V0 + V0 a ?T
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

39. Rotation matrix (2x2)
Cos[?] Sin[?] -Sin[?] Cos[?]
F = f* (c+v_r)/(c+v_s)
I = -(c ?t)^2 + d^2
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

40. Perturbations
Z = ?g_i*exp(-E/kT)
P +1/2 ? v² + ?gh = Constant
H = H_0 + ?H
I = I_0 Cos[?]^2

41. Relativistic Energy
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
?mc²
Measurements close to mean
V = -L di/dt

42. td(entropy) =
PdV +dU
dU = 0 ? dS = ?dW/T
µ0 I1I2 / (2pd)
1/ne - where n is charge carrier density

43. Kepler'S third law (T and R)
T^2 = k R^3 - k=constant
Int ( A . dr) = Int ( del x A) dSurface
ma + kx = 0
? exp(-e/t)

44. 3 Laws of Thermo
Faraday/Lenz: current inducted opposes the changing field
C_eq = (? 1/C_i)^-1
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Z²/n² (m_red/m_elec)

45. EM: Method of Images
? exp(-e/t)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
?~T
Opposing charge induced upon conductor

46. Law of Mass Action
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
J/(ne) n: atom density

47. E field of a capacitor (d->0)
Exp(N(µ-e)/t)
E = s/e_0
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
NC?T

48. Virial Theorem
X_L = i?L
L = mr²d?/dt
<T> = 1/2 * <dV/dx>
E²-p²c²

49. Solid: Resistivity of Metal
?~T
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Measurements close to mean
F = -2*m(? x r)

50. Solid: Resistivity of Semi-Conductor
T = I?²/2
?~1/T
W_A < W_I
P/A = s T^4