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. Springs in series/parallel
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.
dU = 0 ? dS = ?dW/T
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

2. SR: Spacetime Interval
Isentropic
ds² = (c*dt)² - ?(x_i)²
µ0 I / 2R
µ=s^2

3. Magnetic field due to a segment of wire
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
?~1/T
V = V0 + V0 a ?T

4. EM: Electromagnetic inertia
Faraday/Lenz: current inducted opposes the changing field
dQ = dW +dU
P² ~ R³
KE = 1/2 * µ (dr/dt)² L = µ r x v

5. Wein'S displacement law for blackbodies (? and T)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
?_max = b/T
J = E s - s = Conductivity - E = Electric field
F_f = µ*F_N

6. Atom: Positronium Reduced Mass
µ = m_e/2
Int ( A . dr) = Int ( del x A) dSurface
Asin(?) = m?
?s = 0 - ?l = ±1

7. Lensmaker Equation - Thin Lens
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
L = T - V dL/dq = d/dt dL/dqdot
V(r) + L²2/2mr²
F = I L X B

8. Lab: Precision of Measurements
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Measurements close to mean
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
ih_barL_z

9. Biot-Savart law
V = -L di/dt
KE = 1/2 * µ (dr/dt)² L = µ r x v
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
P/A = s T^4

10. Thermo: Average Total Energy
E = s/e_0
?_max = b/T
(° of Freedom)kT/2
W_A < W_I

11. Internal Energy of an Ideal Gas
(3/2) n R ?t
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
ih_barL_z
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

12. Center of Mass: Kinetic Energy & Angular Momentum
J/(ne) n: atom density
?mv
Isentropic
KE = 1/2 * µ (dr/dt)² L = µ r x v

13. Hall Coefficient
Always Real
1/ne - where n is charge carrier density
(3/2) n R ?t
PdV +dU

14. Perpendicular axis theorem
F = R/2
?~T
I_z = I_x + I_y (think hoop symmetry)
U - ts = -tlog(Z)

15. Quant: Expectation Value
F = f* (c+v_r)/(c+v_s)
<?|O|?>
A[B -C] + [A -C]B
E²-p²c²

16. Energy in a Capacitor
I = I_cm + (1/2)m d^2
.5 CV²
P² ~ R³
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

17. EM: AC Resonance
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
? = 5/3
F_f = µ*F_N
X_L = X_C or X_total = 0

18. Bernoulli Equation
DW = P dV
P +1/2 ? v² + ?gh = Constant
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.
Q = CVexp(-t/RC)

19. Bar magnets -- direction of B field lines - earth'S B field
µ = Current * Area T = µ x B
V = V0 + V0 a ?T
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
L = T - V dL/dq = d/dt dL/dqdot

20. Focal point of mirrror with curvature
F = R/2
Sin(?) = ?/d
qvb = mv²/R
Opposing charge induced upon conductor

21. Doppler shift for light
F = f* (c+v_r)/(c+v_s)
X_C = 1/(i?C)
V(r) + L²2/2mr²
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

22. Current in resistor in RC circuit
? = h/mv
? = 5/3
I = V/R exp(-t/RC)
4H + 2e- ? He +2? + 6?

23. Lagrangian and Lagrange'S equation
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 = T - V dL/dq = d/dt dL/dqdot
Asin(?) = m?
<T> = 1/2 * <dV/dx>

24. Inductance of Solenoid
M? = 2dsin(?)
Always Real
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

25. EM: Reactance of Inductor
X_L = i?L
T = I?²/2
µ0 I / 2R
Exponentially decreasing radial function

26. EM: Parallel Capacitance
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
C_eq = ?C_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.
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

27. Stark Effect
1/2 CV²
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
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
V = -L di/dt

28. Entropy (# of states - and in terms of other thermo quantities)
S = k ln[O] ; dS = dQ/T
µ0 I1I2 / (2pd)
Z²/n² (m_red/m_elec)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

29. Bragg'S Law of Reflection
Sin(?) = ?/d
U = t^2 d/dt (logZ)
µ=s^2
M? = 2dsin(?)

30. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
Dp/dt = L / (t ?V)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
F = s * T4
1/vLC

31. A reversible process stays..
F = I L X B
Infinitely close to equilibrium at all times
u dm/dt
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

32. Magnetic Field For Current in Long Wire
µ0 I / 2pR
(3/2) n R ?t
V(r) + L²2/2mr²
?_max = b/T

33. Atom: Bohr Theory Ionization
E = Z²*E1
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
V = V0 + V0 a ?T
L = T - V dL/dq = d/dt dL/dqdot

34. Bohr Model: Energy
?max = 2.898 x 10 -³ / T
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Z²/n² (m_red/m_elec)
u dm/dt

35. Thermo: Isothermal
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Infinitely close to equilibrium at all times
T^2 = k R^3 - k=constant
dU = 0 ? dS = ?dW/T

36. Magnetic Field of a long solenoid
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
B = µ0 I n
dU = 0 ? dS = ?dW/T
ds² = (c*dt)² - ?(x_i)²

37. Magnetic Field Through Ring
F = mv²/r
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
µ0 I / 2R
? = 1.22?/D

38. Astro: p-p Chain
4H + 2e- ? He +2? + 6?
Faraday/Lenz: current inducted opposes the changing field
DW/dq
M? = 2dsin(?)

39. Atom: Orbital Config
I ' = I cos²(?)
Z_c = -i/(?C) ; Z_L = i ? L
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
<T> = -<V>/2

40. Thermo: Partition Function
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
(3/2) n R ?t
Z = ?g_i*exp(-E/kT)

41. Stoke'S Theorem
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
v(mean)
Int ( A . dr) = Int ( del x A) dSurface
A[B -C] + [A -C]B

42. Relativistic length contraction
Measurements close to true value
L = L_0 Sqrt[1-v^2/c^2]
? = h/p
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

43. Force on a wire in magnetic field
F = I L X B
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Isentropic
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

44. Rotation matrix (2x2)
Infinitely close to equilibrium at all times
Cos[?] Sin[?] -Sin[?] Cos[?]
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

45. Solid: Resistivity of Semi-Conductor
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
?~1/T
<T> = -<V>/2

46. Partition Function
? exp(-e/t)
Asin(?) = m?
<?|O|?>
P² ~ R³

47. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
C_eq = ?C_i
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
W_A < W_I

48. Virial Theorem
KE = 1/2 * µ (dr/dt)² L = µ r x v
<T> = 1/2 * <dV/dx>
(3/2) n R ?t
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

49. Compton Scattering
Opposing charge induced upon conductor
?? = h/mc * (1-cos(?))
Measurements close to mean
(° of Freedom)kT/2

50. Planck Radiation Law
qvb = mv²/R
Hbar*?³/(p²c³exp(hbar?/t)-1)
(° of Freedom)kT/2
Always Real