PHYS 308 Homework
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   Homework #8: Due Monday, March 30, by 10:00am.

  1. A (-)3.0μC charge is located at the point (x,y)=(10cm,(-)7.0cm). It is located next to the corner of a grounded box so that anything where y≥0 and anything where x≤0 is grounded. Calcualte the potential at the point (x, y)=(2.0cm, -5.0cm), being sure to show your work.
  2. Use Mathematica to draw the unit vectors of the electric field due to the physical situation above. Plot this from x=(-)15cm to (+)15cm, and y=(-)15cm to (+)15cm. Hint: Check out the HeavisideTheta function in Mathematic by plotting these:
    Plot[HeavisideTheta[x], {x, -10, 10}]
    Plot[HeavisideTheta[x]*Sin[x], {x, -10, 10}]
    Plot[HeavisideTheta[x+3]*Sin[x], {x, -10, 10}]
  3. Consider a 45o "grounded wedge" in a cunductor. One side is along the positive x-axis (pointing to the right); the other starts at the origin, and is tilted at a 45o angle above the positive x-axis. Everywhere outside of this wedge is grounded. A (+)5.0μC charge is located at the point (x,y)=(10cm, 4.142cm)=(10cm,10cm*tan(22.5°)--this puts the charge 22.5° above the x-axis. Draw this situation, and carefully place the correct image charges on your drawing that would allow you to calculated the potential everywhere within that wedge. You do not need to calculate anything.
  4. An electron has been ejected from a supernova explosion and has a kinetic energy of 25MeV. Find (a) the speed of this electron (in some convenient units), and (b) the potential difference that the supernova applied to the electron to get it to go this fast.
  5. A proton from out sun hits Jupiter's magnetic field (perpendicularly) with a speed of 1.00x106m/s; assume the average value of this field throughout this problem is 35nT. Find (a) the Larmor radius of this proton's orbit in this field, (b) the Larmor frequency fL with which this proton goes around that circle, and (c) the electromagnetic power that this proton radiates while in this orbit.
  6. A proton with KE=1.0x1016eV is moving perpendicular to an interstellar magnetic field. The radius of curvature of the proton's path is 11 light years (1 light year is the distance light travels in 1 year). (a) What is the strength of the interstellar magnetic field? (b) How long in years does the proton take to make one complete revolution? (c) How long does it take for the proton to radiate away 20% of its original KE (you may assume the power is approx. constant over this time period)?
   That's all for homework #8.