Physics 308 Homework
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Homework #4: Due Friday, February 21, by 5:15pm

  1. Here is an electric field: E={Kxx2y,Kyx3y2} where this only has x- and y-components, and Kx and Ky take care of all constants and units. Find the potential difference Φ between the points (6,0) and (6,9).
  2. Here is an electric field: E=xExy3cos(3x)+yEyx2sin(4y), where Ex=1,200V/m4 and Ey=950V/m3. Find the electric potential difference Φ between the following pairs of points as you go from the first to the second (a) (-3m, 1.5m) to (4m, 1.5m) (b) (4m, 1.5m) to (4m, -5.2m) (c) (4m, -5.2m) to (-3m, -5.2m). Be careful of your signs.
  3. Here is an electric potential: Φ=K⋅x-1/2y5/2, where the constant 'K' is a number with units. (a) Find the general expression (i.e. leave K just as it is) for the electric field E due to this potential. (b) Find the general expression for the charge density ρ due to this potential. (c) If the potential is 2,450 Volts at the point (1.5m, 0.90m) find the numerical value and units of K. (d) Find the numerical value and units of E at the point (2.0m, 0.55m). (e) Find the numerical value and units of the charge density ρ at the point (2.0m, 0.55m).
  4. Here is a spherically symmetric electric potential: Φ=K⋅r5 where the constant 'K' is a number with units. (a) Find the general expression (i.e. leave K just as it is) for the electric field E due to this potential. (b) Find the general expression for the charge density ρ due to this potential. (c) If the potential is 1,440 Volts at a distance of 3.5m from the origin, find the numerical value and units of K.
   That's all for homework #4.