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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. EM: Electromagnetic inertia
.5 LI²
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Faraday/Lenz: current inducted opposes the changing field
dU = 0 ? dS = ?dW/T

2. EM: SHO (Hooke)
W_A < W_I
ma + kx = 0
?mv
I = I_cm + (1/2)m d^2

3. Bar magnets -- direction of B field lines - earth'S B field
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
?mv
µ=s^2
E = <?| H |?>

4. Thermo: Adiabatic Work vs Isothermal Work
W_A < W_I
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Dp/dt = L / (t ?V)
A[B -C] + [A -C]B

5. Perpendicular axis theorem
F = µ0 q v I / 2pr
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
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.
I_z = I_x + I_y (think hoop symmetry)

6. Solid: Resistivity of Metal
ma + kx = 0
?~T
I = I_cm + (1/2)m d^2
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

7. Single Slit Diffraction Maximum
µ0 I / 2R
Asin(?) = m?
V = V0 + V0 a ?T
DW/dq

8. Commutator identities ( [B -A C] - [A -B] )
Asin(?) = m?
T = I?²/2
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
? = 1.22? / d

9. Work done on a gas
Const: 2t = (n +.5)? Destructive 2t = n?
H = H_0 + ?H
L = L_0 Sqrt[1-v^2/c^2]
DW = P dV

10. How to derive cylcotron frequency
qvb = mv²/R
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Infinitely close to equilibrium at all times
W_A < W_I

11. Springs in series/parallel
1/ne - where n is charge carrier density
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
PdV +dU
Isentropic

12. Focal point of mirrror with curvature
Measurements close to mean
F = R/2
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

13. Rocket Equation
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Const: 2t = (n +.5)? Destructive 2t = n?
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Dv = -udm/m - v = v0 + u ln(m0/m)

14. Double Slit: Interference Minimum - Diffraction Minimum
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
F = R/2
? = 1.22?/D

15. Magnetic field due to a segment of wire
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
P/A = s T^4
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

16. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
?_max = b/T
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
C_eq = (? 1/C_i)^-1
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

17. Effective Potential
.5 CV²
V(r) + L²2/2mr²
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I_z = I_x + I_y (think hoop symmetry)

18. Partition Function
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
? exp(-e/t)
PdV +dU
P/A = s T^4

19. SR: Total Energy of a Particle
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Faraday/Lenz: current inducted opposes the changing field
PdV +dU
Exponentially decreasing radial function

20. De Broigle Wavelength
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I_z = I_x + I_y (think hoop symmetry)
? = h/mv
E = <?| H |?>

21. Biot-Savart law
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
F = f* (c+v_r)/(c+v_s)
P1V1 - P2V2 / (? - 1)
U - ts = -tlog(Z)

22. Quant: [L_x -L_y] = ?
M? = 2dsin(?)
ih_barL_z
0
V(r) + L²2/2mr²

23. Rocket Thrust
u dm/dt
1/ne - where n is charge carrier density
? = h/mv
X_L = X_C or X_total = 0

24. E field of a capacitor (d->0)
Braking Radiation
Ct²-x²-y²-z²
E = s/e_0
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

25. EM: Bremsstrahlung (translation)
A[B -C] + [A -C]B
? = ?0 root((1-v/c)/(1+v/c))
Braking Radiation
Measurements close to mean

26. Angular momentum operators L^2 and L_z
<?|O|?>
Int ( A . dr) = Int ( del x A) dSurface
Exponentially decreasing radial function
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

27. RLC resonance condition
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
µ = Current * Area T = µ x B
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

28. Quant: Orthogonality of States
<?1|?2> = 0 ? Orthogonal
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
M? = 2dsin(?)
Dv = -udm/m - v = v0 + u ln(m0/m)

29. Current in resistor in RC circuit
L = mr²d?/dt
I = V/R exp(-t/RC)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
DS = 0 - dQ = 0 - P V^? = constant

30. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
T = I?²/2
Isentropic

31. Helmholtz Free Energy
Dv = -udm/m - v = v0 + u ln(m0/m)
F = f* (c+v_r)/(c+v_s)
U - ts = -tlog(Z)
L = mr²d?/dt

32. Work (P - V)
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.
P1V1 - P2V2 / (? - 1)
A[B -C] + [A -C]B
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

33. Thermo: Monatomic gas ?=?
? = 5/3
NC?T
?~T
M? = 2dsin(?)

34. Astro: p-p Chain
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
4H + 2e- ? He +2? + 6?
?~T
E = <?| H |?>

35. Quant: Eigenvalue of Hermitian Operator
L = T - V dL/dq = d/dt dL/dqdot
Always Real
? = ?0 root((1-v/c)/(1+v/c))
P +1/2 ? v² + ?gh = Constant

36. Electromotive Force
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Faraday/Lenz: current inducted opposes the changing field
V = V0 + V0 a ?T
DW/dq

37. Atom: Bohr Formula
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
X_L = i?L
KE = 1/2 * µ (dr/dt)² L = µ r x v
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

38. Quant: Expectation Value
.5 LI²
I = -(c ?t)^2 + d^2
Measurements close to true value
<?|O|?>

39. Doppler Shift for light
I = I_cm + md²
µ0 I / 2R
P² ~ R³
? = ?0 root((1-v/c)/(1+v/c))

40. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
? exp(-e/t)
(3/2) n R ?t
1/2 CV²

41. Virial Theorem
?mv
<T> = 1/2 * <dV/dx>
? = 1.22?/D
1/2 CV²

42. Delta Function Potential - type of WF
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
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
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
V = -L di/dt

43. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
? = ?0 root((1-v/c)/(1+v/c))
N²/Z (m_elec/m_red)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

44. Center of Mass: Kinetic Energy & Angular Momentum
KE = 1/2 * µ (dr/dt)² L = µ r x v
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Q = CVexp(-t/RC)
dU = 0 ? dS = ?dW/T

45. Adiabatic processes (dS - dQ - P and V)
qvb = mv²/R
Dv = -udm/m - v = v0 + u ln(m0/m)
v(mean)
DS = 0 - dQ = 0 - P V^? = constant

46. A reversible process stays..
µ = m_e/2
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Infinitely close to equilibrium at all times
Opposing charge induced upon conductor

47. Mech: Rotational Energy
Exponentially decreasing radial function
I = I_cm + (1/2)m d^2
DS = 0 - dQ = 0 - P V^? = constant
T = I?²/2

48. Induced EMF of solenoid
S = (hbar/2) s ;with S = S_x xhat + S_y yhat + S_z zhat -s = s_x xhat + s_y yhat + s_z zhat
DW/dq
N d flux / dt
Dv = -udm/m - v = v0 + u ln(m0/m)

49. EM: Series Capacitance
P +1/2 ? v² + ?gh = Constant
Dp/dt = L / (t ?V)
C_eq = (? 1/C_i)^-1
? = ?0 root((1-v/c)/(1+v/c))

50. Bohr Model: Radii
Z²/n² (m_red/m_elec)
F_f = µ*F_N
? = 1.22? / d
N²/Z (m_elec/m_red)