1. Two point-charges +q are located at positions x = ±a, y = 0, z = 0 in free space. The black solid lines show the electric field and the red dashed lines represent the equipotential curves for this electric dipole. (a) Derive the electric potential on the x axis. Determine the point where the potential is zero. (b) Prove that at long distances (r≫ a), the electric potential is proportional with 1/r²./n(Point: 20%) 2. Derive the electric potential generated by a straight line at the distance y above midpoint of the line. Assume that the line has the charge density of 2 and length of 1. Answer: (Point: 15%) λ In Απερ (l/2)+(l/2) + y² -(l/2) + √(l/2)² + y² 3. A right isosceles triangle of side a has charges q, +2q and -q arranged on its vertices. y 9 a a 29 -9/n(a) What is the electric potential at point P, midway between the line connecting the +q and -q charges, assuming that V = 0 at infinity? [Ans: q/√2 лεa.] (b) What is the potential energy U of this configuration of three charges? What is the significance of the sign of your answer? [Ans: -q2/4√2 лεa, the negative sign means that work was done on the agent who assembled these charges in moving them in from infinity.] (Point: 15%) 4. A dielectric sphere with relative permittivity of ε, and radius of R is charged with uniform volume charge density of p. Using Gauss' law, derive the electric field, E, and by integrating the electric field derive the electric potential inside and outside of the sphere. Plot the electric potential versus distance and discuss the boundary condition. R 2 ε Eo (Free space) (Point: 20%) 5. A point charge Q is located at (x, y, z) = (0, 0, d) above an infinite grounded conductive plane defined by z = 0. Using the method of images, derive electric potential at the the point (x, y, z) = (0, 0, d/2) above the plane. (Point: 15%) 6. Summarize the most important concepts and theories you have learned in this chapter in a maximum of one page. (Points: 15%)

Fig: 1

Fig: 2

Fig: 3