PHYS 308 Homework
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   Homework #4: Due Friday, February 20, by 5:00pm.

  1. 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).
  2. 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.
  3. Here is a spherically symmetric charge distribution: ρ=K r5 where K=1.00x10-10C/m8.
       a. Find the general expressions (no numbers yet) for the electric field at an arbitrary distance 'r' from the origin. Note that both the charge density ρ and the electric field E will be spherically symmetric--include the appropriate unit vector for E.
       b. If the magnitude of the electric field at a radial distance r=0.85m from the origin is 1.38N/C, determine the value of the constant that appeared in part (a).
  4. Here is a spherically symmetric charge distribution: ρ=K r6 where K=1.20x10-10C/m9.
       a. Find the general expression for the electric potential Φ due to this charge distribution. Don't forget to include the correct number of integration constants!
       b. Assuming the constants that appeared in part (a) are equal to zero, find the potential Φ at r=1.20m from the origin.
   That's all for homework #4.