Test your basic knowledge |

GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Stefan-Boltzmann law for blackbodies (power per area and T)
P/A = s T^4
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
? = 5/3
Measurements close to mean

2. td(entropy) =
?~T
ma + kx = 0
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
PdV +dU

3. Energy in terms of partition function
?mv
? = 1.22?/D
U = t^2 d/dt (logZ)
PdV +dU

4. Pauli matrices
P² ~ R³
I = Im (sinc²(a)) ; a = pai sin(?) / ?
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

5. Weighted average (mean and unc. of mean)
Measurements close to mean
I = V/R exp(-t/RC)
.5 LI²
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

6. Malus Law

7. Bohr Model: Radii
Measurements close to mean
N²/Z (m_elec/m_red)
DW/dq
PdV +dU

8. Bohr Model: Energy
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
N²/Z (m_elec/m_red)
Z²/n² (m_red/m_elec)
F_f = µ*F_N

9. SR: Spacetime Interval
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
P +1/2 ? v² + ?gh = Constant
ds² = (c*dt)² - ?(x_i)²
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

10. Virial Theorem
<T> = 1/2 * <dV/dx>
I ' = I cos²(?)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
T = I?²/2

11. Selection rules for atomic transitions
?? = h/mc * (1-cos(?))
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
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
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

12. Thermo: Adiabatic Work vs Isothermal Work
W_A < W_I
ds² = (c*dt)² - ?(x_i)²
V(r) + L²2/2mr²
Measurements close to mean

13. Selection Rules
I = I_cm + md²
N d flux / dt
M? = 2dsin(?)
?s = 0 - ?l = ±1

14. Error in the mean if each measurement has the same uncertainty s
L = L_0 Sqrt[1-v^2/c^2]
P/A = s T^4
V = -L di/dt
S_mean = s/Sqrt[N]

15. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
Const: 2t = (n +.5)? Destructive 2t = n?
E²-p²c²
µ0 I1I2 / (2pd)

16. Inductance 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
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
M? = 2dsin(?)
Measurements close to mean

17. Magnetic Field For Current in Long Wire
v(mean)
Z = ?g_i*exp(-E/kT)
<T> = -<V>/2
µ0 I / 2pR

18. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
?max = 2.898 x 10 -³ / T
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
J = ? Fdt

19. De Broglie wavelength
F = -2*m(? x r)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
? = h/p
ds² = (c*dt)² - ?(x_i)²

20. Self Inductance
U - ts = -tlog(Z)
µ0 I1I2 / (2pd)
V = -L di/dt
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

21. Lab: Standard Deviation of Poisson
L = mr²d?/dt
F = f* (c+v_r)/(c+v_s)
v(mean)
Exponentially decreasing radial function

22. Mean electron drift speed
KE = 1/2 * µ (dr/dt)² L = µ r x v
J/(ne) n: atom density
dQ = dW +dU
Always Real

23. Rocket Equation
v(mean)
U - ts = -tlog(Z)
Dv = -udm/m - v = v0 + u ln(m0/m)
Ct²-x²-y²-z²

24. SR: Total Energy of a Particle
J = E s - s = Conductivity - E = Electric field
J = ? Fdt
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
J/(ne) n: atom density

25. First law of thermodynamics (explain direction of energy for each term)
Faraday/Lenz: current inducted opposes the changing field
KE = 1/2 * µ (dr/dt)² L = µ r x v
? = 1.22?/D
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

26. Quant: Commutator Relation [AB -C]
u dm/dt
A[B -C] + [A -C]B
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
X_C = 1/(i?C)

27. Spherical Capacitor Equation
? = 1.22?/D
NC?T
C = 4pe0 ab/(a-b) = inner and outer radii
Ct²-x²-y²-z²

28. RLC resonance condition
Int ( A . dr) = Int ( del x A) dSurface
Dv = -udm/m - v = v0 + u ln(m0/m)
Z_c = -i/(?C) ; Z_L = i ? L
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

29. Thin Film Theory: Constructive / Destructive Interference
Sin(?) = ?/d
Const: 2t = (n +.5)? Destructive 2t = n?
X_L = i?L
U - ts = -tlog(Z)

30. Complex impedance (expressions for capacitor and inductor)
Cos[?] Sin[?] -Sin[?] Cos[?]
F = s * T4
Z_c = -i/(?C) ; Z_L = i ? L
F = -2*m(? x r)

31. Energy in Inductor
C_eq = ?C_i
.5 LI²
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
0

32. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
?~T
µ = m_e/2
1/vLC

33. Angular momentum - Central Force Motion
X_C = 1/(i?C)
P/A = s T^4
L = mr²d?/dt
.5 CV²

34. Resonance frequency of LC circuit
1/ne - where n is charge carrier density
B = µ0 I n
1/vLC
µ=s^2

35. Rayleigh criterion
? = 1.22? / d
0
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
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.

36. Atom: Bohr Theory Ionization
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
E = Z²*E1
µ0 I / 2R
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

37. Quant: Expectation Value
<?|O|?>
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
W_A < W_I
Int ( A . dr) = Int ( del x A) dSurface

38. Invariant spatial quantity
µ0 I / 2R
I = I_cm + md²
? = h/mv
Ct²-x²-y²-z²

39. Atom: Hydrogen Wave Function Type
dU = 0 ? dS = ?dW/T
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
U - ts = -tlog(Z)
Exponentially decreasing radial function

40. Bernoulli Equation
F = qv×B
P +1/2 ? v² + ?gh = Constant
P² ~ R³
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

41. Focal point of mirrror with curvature
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
µ0 I1I2 / (2pd)
F = R/2
Dv = -udm/m - v = v0 + u ln(m0/m)

42. Relativistic Momentum
Sin(?) = ?/d
?mv
F = f* (c+v_r)/(c+v_s)
F_f = µ*F_N

43. Charge in Capacitor
µ0 I / 2R
.5 LI²
Q = CVexp(-t/RC)
F = I L X B

44. Wein'S displacement law for blackbodies (? and T)
u dm/dt
?_max = b/T
Dv = -udm/m - v = v0 + u ln(m0/m)
Const: 2t = (n +.5)? Destructive 2t = n?

45. 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.
.5 CV²
E = Z²*E1
v(mean)

46. Entropy (# of states - and in terms of other thermo quantities)
?s = 0 - ?l = ±1
? = 1.22?/D
F = R/2
S = k ln[O] ; dS = dQ/T

47. Quant: Orthogonality of States
<?1|?2> = 0 ? Orthogonal
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
4H + 2e- ? He +2? + 6?

48. Magnetic Dipole Moment and Torque
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Measurements close to true value
µ = Current * Area T = µ x B
? (t-vx/c²)

49. Dulong Petit Law
? = 1.22? / d
?= h/v(2mE)
Faraday/Lenz: current inducted opposes the changing field
Cv = dE/dT = 3R

50. Force/length between two wires
?~T
Sin(?) = ?/d
µ0 I1I2 / (2pd)
C = 4pe0 ab/(a-b) = inner and outer radii