Ph110B-15:

Part a (10 points) : B due to a solenoid: 0 outside, mu_0 n I \zhat inside

   120 %: practically perfect + good symmetry argument using pseudo-vector
   110 %: practically perfect + good symmetry argument using pseudo-vector
          (but with error)
   100 %: practically perfect
    80 %: direction of B, only half explained
    80 %: correct starting point for explaning the direction of B, not
          followed through
    80 %: all OK, except that the reason for B = 0 outside is not good
    60 %: direction of B not explained
    25 %: correct answer stated with no derivation
    25 %: some discussion but no clear derivation of either direction or
          magnitude

Part b (10 points) :

   100 %: practically perfect
    85 %: correct except for a sign mistake
    80 %: everthing OK, but dimensions for x(t) and y(t) are incorrect due
          to a dropped symbol
    70 %: concluded uniform circular motion, but did not really prove it
          (integration constants not related)
    60 %: integration constants for x(t) and y(t) are not/incorrectly
          related
    50 %: said circular motion, but the solutions for x(t) and y(t) cannot
          be that; omega is OK
    40 %: qualitative answer only and no answer for what omega is
    33 %: got an exponential function or a quadratic function rather than
          sinusoidal function
    25 %: correct starting formula, but no or little development from it

Part c (10 points) :

   100 %: practically perfect
    70 %: The dervivation for E = v x B has a serious hole.
    50 %: E is good, but B is not discussed
    50 %: B is correct, but E is completely wrong
    25 %: correct starting formula, but no or little development from it
    10 %: some discussion is presented, but no clear direction is indicated

Part d (10 points) :

   100 %: practically perfect
    60 %: qualitatively correct discussion, but no showing that centrifugal
          foce = |qE|
    50 %: centripetal force is OK, but the centrifugal force is not
          discussed correctly
    10 %: some discussion is presented, but no clear direction is indicated
     0 %: answer missing, or completely incorrect

Part e (10 points) :

   100 %: practically perfect
    90 %: correct formulas, mangled by wrong substitution for \vec r
    80 %: correct starting point for A and V, but major mistakes were made
          (wrong time dependence, e.g.)
     0 %: answer missing, or completely incorrect

Part f (10 points) : accel or vel = sin or cos (kx - omega_c t + phi_0)

   100 %: practically perfect
    60 %: correct answer but the reason is not enough (noted only the t
          dependence of phase)
    33 %: correct answer deduced from insufficient reasons or incorrect
          reasons
    25 %: correct starting formula, but no or little development from it
     0 %: answer missing, or completely incorrect

Part g (10 points) : S has two components (// rhat (rad) and perp. to rhat)

   100 %: practically perfect
    95 %: both terms are present, but the angular dependence is completely
          wrong
    90 %: correct starting formula, but no or little development from it
    90 %: got radiation term only, which is also incorrect
    90 %: completely wrong, but due to a previous mistake in part e
    90 %: got radiation term only
     0 %: answer missing, or completely incorrect

Part h (10 points) : Eq. 11.59 with appropriate |\ddot p(t0)|

   100 %: practically perfect
    90 %: correct except for a (small) numerical error
    70 %: expression OK, except for the angular dependence
    70 %: expression OK, except that it has spurious time-dependence
    60 %: expression OK, except that a (acceleration) is not explained
    50 %: incorrect angular dependence and unexplained a
    40 %: incorrect direction, incorrect angular dependence
    25 %: correct starting formula, but no or little development from it
     0 %: answer missing, or completely incorrect

Part i (10 points) : (g) is the same as (h) if only the radiation term is
                     taken

   100 %: practically perfect
    90 %: correct except for a (small) numerical error
    70 %: managed to show the equivalence, but with spurious t-dependence
    60 %: misundertood symbols and could not prove the equivalence
    40 %: correct starting formula but could not convert the formula to
          show that it is the same as the ans of h (even if the agreement
          was "argued for")
    25 %: correct starting formula, but no or little development from it
     0 %: answer missing, or completely incorrect

Part j (10 points) : Eq. 11.60 with |\ddot p(t0)| replaced properply

   100 %: practically perfect
    90 %: correct except for a (small) numerical error
    80 %: got an incorrect answer dimensionally due to a simple mistake in
          power
    80 %: expression is OK, except that a (acceleration) is not explained
    80 %: got a formula that is t-dependent incorrectly
    50 %: answer contains integration mistake and unexplained a
    33 %: serious integration mistake caused answer dependent on r
    25 %: correct starting formula, but no or little development from it
     0 %: answer missing, or completely incorrect

Part k (10 points) : omega_c --> omega_c / \gamma where omega_c = that of
                     (b)

   100 %: practically perfect
    85 %: correct except for a sign mistake
    75 %: all is OK, except that y(t) has an incorrect term (like linear-
          in-t term)
    60 %: omega_c is incorrect; OK otherwise
    60 %: omega_c is correct but integration constants are not correctly
          related
    60 %: omega_c is correct but equation of motion is not solved or is
          incorrectly solved
    50 %: forgot the gamma factor for p
    50 %: omega_c is incorrect and there is a sign error
    50 %: omega_c is incorrect and the equation of motion is not solved or
          is incorrectly solved
    33 %: qualitatively argued "the same motion," which is incorrect
    25 %: correct starting formula, but no or little development from it
    10 %: some discussion is presented, but no clear direction is indicated
     0 %: answer missing, or completely incorrect

Part l (10 points) :

   100 %: practically perfect
    50 %: B is correct (at least in relation to B_lab), but E is incorrect
    50 %: B is incorrect, while E is correct (at least in relation to B)
    33 %: E and B are computeed incorrectly from Lorentz transform
    33 %: E and B are computed incorrecly from the field tensor
    25 %: correct starting formula, but no or little development from it
    10 %: some discussion is presented, but no clear direction is indicated
     0 %: answer missing, or completely incorrect

Part m (10 points) :

   100 %: practically perfect (qualitative discussion only)
    10 %: some discussion is presented, but no clear direction is indicated
     0 %: answer missing, or completely incorrect
UC Santa Cruz Department of Physics