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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 for orbits: Hyperbole - Ellipse - Parabola - Circle
DW = P dV
X_L = i?L
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
I ' = I cos²(?)

2. Adiabatic means
T = I?²/2
M? = 2dsin(?)
Isentropic
qvb = mv²/R

3. Magnetic Field of a long solenoid
J = ? Fdt
B = µ0 I n
µ = Current * Area T = µ x B
I = I_cm + md²

4. Magnetic Field Through Ring
Const: 2t = (n +.5)? Destructive 2t = n?
µ0 I / 2R
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
W_A < W_I

5. Work (P - V)
Cos[?] Sin[?] -Sin[?] Cos[?]
P1V1 - P2V2 / (? - 1)
C_eq = (? 1/C_i)^-1
M? = 2dsin(?)

6. Wein'S displacement law for blackbodies (? and T)
<?1|?2> = 0 ? Orthogonal
?_max = b/T
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Ct²-x²-y²-z²

7. Double Slit: Interference Minimum - Diffraction Minimum
?s = 0 - ?l = ±1
E = <?| H |?>
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
? exp(-e/t)

8. Quant: Expectation Value
N d flux / dt
<?|O|?>
Const: 2t = (n +.5)? Destructive 2t = n?
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

9. SR: Spacetime Interval
.5 CV²
µ0 I / 2R
PdV +dU
ds² = (c*dt)² - ?(x_i)²

10. EM: Parallel Capacitance
C_eq = ?C_i
P/A = s T^4
Z = ?g_i*exp(-E/kT)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

11. Helmholtz Free Energy
?? = h/mc * (1-cos(?))
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I = I_cm + (1/2)m d^2
U - ts = -tlog(Z)

12. EM: Method of Images
?_max = b/T
<T> = 1/2 * <dV/dx>
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Opposing charge induced upon conductor

13. Angular momentum operators L^2 and L_z
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Int ( A . dr) = Int ( del x A) dSurface
J/(ne) n: atom density
?s = 0 - ?l = ±1

14. How to derive cylcotron frequency
P/A = s T^4
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
X_C = 1/(i?C)
qvb = mv²/R

15. Rocket Thrust
A[B -C] + [A -C]B
u dm/dt
J/(ne) n: atom density
E²-p²c²

16. Self Inductance
F_f = µ*F_N
F = mv²/r
I = I_0 Cos[?]^2
V = -L di/dt

17. EM: SHO (Hooke)
I = V/R exp(-t/RC)
ma + kx = 0
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
X_C = 1/(i?C)

18. Dulong Petit Law
1/2 CV²
J/(ne) n: atom density
Dp/dt = L / (t ?V)
Cv = dE/dT = 3R

19. Force exerted on charge by long wire
Exponentially decreasing radial function
F = µ0 q v I / 2pr
Braking Radiation
Cos[?] Sin[?] -Sin[?] Cos[?]

20. Boltzmann / Canonical distribution
H = H_0 + ?H
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Isentropic
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

21. Doppler Shift for light
P1V1 - P2V2 / (? - 1)
? = ?0 root((1-v/c)/(1+v/c))
? = h/mv
I = I_cm + md²

22. Doppler shift for light
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
?mv
V(r) + L²2/2mr²

23. Focal point of mirrror with curvature
F = R/2
Asin(?) = m?
A[B -C] + [A -C]B
Hbar*?³/(p²c³exp(hbar?/t)-1)

24. Atom: Bohr Formula
U = t^2 d/dt (logZ)
Always Real
C_eq = (? 1/C_i)^-1
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

25. Atom: Hydrogen Wave Function Type
Sin(?) = ?/d
? = h/mv
Exponentially decreasing radial function
J/(ne) n: atom density

26. Poisson distribution (µ and s)
Q = CVexp(-t/RC)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
µ=s^2

27. EM: Electric Field inside of Conductor
0
I = I_cm + md²
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
I = Im (sinc²(a)) ; a = pai sin(?) / ?

28. Selection rules for atomic transitions
C = 4pe0 ab/(a-b) = inner and outer radii
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

29. Solid: Resistivity of Metal
1/2 CV²
?~T
S_mean = s/Sqrt[N]
F = µ0 q v I / 2pr

30. Radiation (Larmor - and another neat fact)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
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.
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

31. Rotation matrix (2x2)
Faraday/Lenz: current inducted opposes the changing field
L = T - V dL/dq = d/dt dL/dqdot
Cos[?] Sin[?] -Sin[?] Cos[?]
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

32. Mech: Force of Friction
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.
F_f = µ*F_N
dQ = dW +dU
u dm/dt

33. Magnetic field due to a segment of wire
v(mean)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
DW = P dV
F = s * T4

34. Selection Rules
T^2 = k R^3 - k=constant
<T> = 1/2 * <dV/dx>
?s = 0 - ?l = ±1
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

35. Quant: [L_x -L_y] = ?
? = h/p
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
X_C = 1/(i?C)
ih_barL_z

36. Stark Effect
Z_c = -i/(?C) ; Z_L = i ? L
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
I = I_cm + md²
KE = 1/2 * µ (dr/dt)² L = µ r x v

37. Induced EMF of solenoid
N d flux / dt
S_mean = s/Sqrt[N]
E = s/e_0
Z_c = -i/(?C) ; Z_L = i ? L

38. Mech: Rotational Energy
? = 1.22?/D
H = H_0 + ?H
T = I?²/2
<?|O|?>

39. Resonance frequency of LC circuit
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
I_z = I_x + I_y (think hoop symmetry)
?mc²
1/vLC

40. Polarizers - intensity when crossed at ?
Z = ?g_i*exp(-E/kT)
Ct²-x²-y²-z²
I = I_0 Cos[?]^2
E = <?| H |?>

41. Thermo: Average Total Energy
(° of Freedom)kT/2
I = I_0 Cos[?]^2
.5 LI²
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

42. Compton Scattering
DW/dq
?? = h/mc * (1-cos(?))
Always Real
u dm/dt

43. Bragg'S Law of Reflection
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
M? = 2dsin(?)
E = Z²*E1

44. Perpendicular axis theorem
N²/Z (m_elec/m_red)
Hbar*?³/(p²c³exp(hbar?/t)-1)
Asin(?) = m?
I_z = I_x + I_y (think hoop symmetry)

45. Law of Mass Action
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
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
S = k ln[O] ; dS = dQ/T
Dv = -udm/m - v = v0 + u ln(m0/m)

46. Bar magnets -- direction of B field lines - earth'S B field
P +1/2 ? v² + ?gh = Constant
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

47. EM: Lorentz Force
F = f* (c+v_r)/(c+v_s)
µ = m_e/2
F = R/2
F = qv×B

48. Thermo: Monatomic gas ?=?
? = 5/3
? (t-vx/c²)
I_z = I_x + I_y (think hoop symmetry)
?max = 2.898 x 10 -³ / T

49. Springs in series/parallel
I = I_cm + (1/2)m d^2
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

50. Inductance of Solenoid
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
F = mv²/r
? = h/p
? = 1.22?/D