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. Doppler shift for light
? = 5/3
.5 CV²
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

2. Atom: Bohr Theory Ionization
Exponentially decreasing radial function
ma + kx = 0
DS = 0 - dQ = 0 - P V^? = constant
E = Z²*E1

3. Stoke'S Theorem
Always Real
DW/dq
Int ( A . dr) = Int ( del x A) dSurface
µ0 I / 2R

4. Volumetric Expansion
V = V0 + V0 a ?T
µ=s^2
F = qv×B
I = V/R exp(-t/RC)

5. Relativistic Energy
?mc²
? = ?0 root((1-v/c)/(1+v/c))
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

6. Time Lorentz Transformation
U = t^2 d/dt (logZ)
X_C = 1/(i?C)
Cos[?] Sin[?] -Sin[?] Cos[?]
? (t-vx/c²)

7. Law of Mass Action
?mv
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
<?|O|?>
DW = P dV

8. Clausius-Clapeyron Equation
dQ = dW +dU
F = -2*m(? x r)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Dp/dt = L / (t ?V)

9. Relativistic Momentum
F = µ0 q v I / 2pr
?mv
P1V1 - P2V2 / (? - 1)
?? = h/mc * (1-cos(?))

10. Magnetic field due to a segment of wire
C_eq = (? 1/C_i)^-1
U = t^2 d/dt (logZ)
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Exp(N(µ-e)/t)

11. Mech: Force of Friction
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
F_f = µ*F_N
?? = h/mc * (1-cos(?))

12. Quant: Expectation Value
<?|O|?>
Dp/dt = L / (t ?V)
? = 1.22?/D
M? = 2dsin(?)

13. Biot-Savart law
Z²/n² (m_red/m_elec)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
?s = 0 - ?l = ±1

14. SR: Spacetime Interval
ds² = (c*dt)² - ?(x_i)²
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
1/ne - where n is charge carrier density

15. Bohr Model: Energy
Z²/n² (m_red/m_elec)
?~T
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
? = 5/3

16. Thermo: Monatomic gas ?=?
? = 5/3
C_eq = ?C_i
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
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.

17. Atom: Bohr Formula
J = ? Fdt
L = L_0 Sqrt[1-v^2/c^2]
E = Z²*E1
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

18. Doppler Shift for light
F = f* (c+v_r)/(c+v_s)
? = ?0 root((1-v/c)/(1+v/c))
ih_barL_z
V = -L di/dt

19. Bernoulli Equation
X_L = X_C or X_total = 0
µ0 I / 2pR
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
P +1/2 ? v² + ?gh = Constant

20. A reversible process stays..
Infinitely close to equilibrium at all times
E = <?| H |?>
<?1|?2> = 0 ? Orthogonal
dQ = dW +dU

21. Error in the mean if each measurement has the same uncertainty s
S_mean = s/Sqrt[N]
Opposing charge induced upon conductor
Sin(?) = ?/d
? = 1.22?/D

22. 3 Laws of Thermo
Measurements close to true value
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
?max = 2.898 x 10 -³ / T

23. Malus Law

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

24. Angular momentum - Central Force Motion
X_L = X_C or X_total = 0
F = qv×B
L = mr²d?/dt
0

25. Hall Coefficient
E²-p²c²
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
1/ne - where n is charge carrier density
U = t^2 d/dt (logZ)

26. Dulong Petit Law
Faraday/Lenz: current inducted opposes the changing field
V(r) + L²2/2mr²
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Cv = dE/dT = 3R

27. Pauli matrices
? exp(-e/t)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
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
Exponentially decreasing radial function

28. Invariant spatial quantity
Ct²-x²-y²-z²
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Always Real
? exp(-e/t)

29. EM: Series Capacitance
u dm/dt
? = 5/3
C_eq = (? 1/C_i)^-1
T = I?²/2

30. Selection Rules
DW = P dV
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
?s = 0 - ?l = ±1
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

31. Boltzmann / Canonical distribution
Cv = dE/dT = 3R
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
V(r) + L²2/2mr²
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

32. Focal point of mirrror with curvature
V = -L di/dt
Ct²-x²-y²-z²
F = µ0 q v I / 2pr
F = R/2

33. Thermo: Adiabatic Work vs Isothermal Work
W_A < W_I
P1V1 - P2V2 / (? - 1)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Z²/n² (m_red/m_elec)

34. Expectation value of the energy of state |?>
F = s * T4
E = <?| H |?>
Asin(?) = m?
X_L = i?L

35. Commutator identities ( [B -A C] - [A -B] )
DW/dq
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
? = 1.22?/D
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

36. Kepler'S Three Laws
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
? = ?0 root((1-v/c)/(1+v/c))
C = 4pe0 ab/(a-b) = inner and outer radii
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

37. Adiabatic processes (dS - dQ - P and V)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
ds² = (c*dt)² - ?(x_i)²
DS = 0 - dQ = 0 - P V^? = constant
? = h/p

38. Mech: Impulse
DW = P dV
µ = Current * Area T = µ x B
NC?T
J = ? Fdt

39. Poisson distribution (µ and s)
µ0 I1I2 / (2pd)
µ=s^2
E = s/e_0
I = -(c ?t)^2 + d^2

40. Thermo: Blackbody Radiation
µ0 I / 2pR
? = h/p
C_eq = (? 1/C_i)^-1
F = s * T4

41. Resistance - length - area - rho
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
N d flux / dt
I_z = I_x + I_y (think hoop symmetry)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

42. Addition of relativistic velocities

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

43. Induced EMF of solenoid
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
KE = 1/2 * µ (dr/dt)² L = µ r x v
N d flux / dt
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

44. Doppler Shift in Frequency
I = Im (sinc²(a)) ; a = pai sin(?) / ?
F = µ0 q v I / 2pr
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
F = f* (c+v_r)/(c+v_s)

45. Perpendicular axis theorem
Sin(?) = ?/d
I_z = I_x + I_y (think hoop symmetry)
J = E s - s = Conductivity - E = Electric field
F = -2*m(? x r)

46. EM: Parallel Capacitance
C_eq = ?C_i
W' = (w-v)/(1-w v/c^2) ; observer in S sees an object moving at velocity w; another frame S' moves at v wrt S.
P1V1 - P2V2 / (? - 1)
I = I_cm + md²

47. Spherical Capacitor Equation
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
C = 4pe0 ab/(a-b) = inner and outer radii
F = I L X B
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

48. Solid: Resistivity of Metal
S = k ln[O] ; dS = dQ/T
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
?~T
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

49. Inductance of Solenoid
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
M? = 2dsin(?)
PdV +dU

50. RLC resonance condition
W' = (w-v)/(1-w v/c^2) ; observer in S sees an object moving at velocity w; another frame S' moves at v wrt S.
F = µ0 q v I / 2pr
Ct²-x²-y²-z²
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]