× 10-4C. Assume that Coulomb’s constant, (k) is equal to 9.0×109 N × m2/c2 a) Determine the total electric potential energy for the charge distribution. b) Determine the total electric potential at point Z.

2. A charge q = - 2.0 C moves in the opposite direction of a uniform electric field of 100 V/m by a distance of 3.0m. a. The charge is at a point of (a. higher, b. lower, c. same) potential before moving. b. After moving, the potential energy of the charge a. increases. b. decreases. c. does not change. c. What is the change in the potential energy?

5. The Poisson equation 8² + ax² ay² az² relates the electrostatic potential (r) = (x, y, z) to the charge distribution p(r) in vacuum. In partic- ular, when we are dealing with a point charge, we write this equation as 7²4 = | 8² əx² + 8² 8² əz² 2² + o(r) + G 5, 8) = - = 10² G(r, r') p(r) €0 -83) (r-r'), where r' = (x, y, z) is the position of the point charge, 63) (r - r') = 6(x − x')8(y - y')6(z - z') is the Dirac delta function in three-dimensional space. Solve for G(r, r') by performing a three-dimensional Fourier transform on the Poisson equation, followed by a three-dimensional inverse Fourier transform. You may use the result 00 sin id=

21. Two metal plates are charged and are measured to have a potential difference of 15.0 V. An electron is placed near the negative plate and released. What is the kinetic energy of the electron when it reaches the positive plate? a. 24.0 x 10¹ b. 9.9 x 10-¹9 1.0 x 10-¹9 J 13.4 x 10-19 j c. d.

1. Two point charges, +3 C and -6 C, are separated by 20 cm. They are NOT free to move. a) What is the magnitude of the electrostatic (Coulomb) force between the charges? Leave your answer as a function of k. ibuenser b) What is the electric field at the center point between the two charges? Leave your answer as a function of k. c) What is the electric potential at the center point between the two charges? Leave your answer as a function of k.

5. You found that the electric potential due to a dipole oriented along the z axis is given by pco$e) 4те a. What is the direction of the field along the x axis? b. If we are on the x axis, a derivative with respect to z is the same as 1 d dz ф Use this equivalence to calculate Ez along the x axis. This should agree with your result from Unit VII p. 20 in your activity guide

A -15 nC charge and a 9 nC charge are located on the x-axis at x=-6 cm and x=9 cm respectively. iii.How far to the left of the -15nC charge does the electric potential equal -27V?   iv.What is the magnitude (in N/C) of the electric field at this location?