Question

Electric potential for a continuous charge distribution: Let's consider a line of charge, of length L having a uniform charge density lambda = 10^-6 C/m and length L=10 cm. Find the electric potential at point P, which is at a distance Z=5 cm. above the midpoint of the line. where In is the natural logarithm. Consider two charged conducting spheres, radii r1 and r2, with charges q1 and q2, respectively. The spheres are far away from each other but connected with a very thin conducting wire. Knowing that the electric field of a charged sphere, outside the sphere is given by where q is the total charge on the sphere and r the distance from the center, calculate the electric potential V(r1) and V(r2) just on the surface of each sphere as a function of (q1, r1) and (q2,r2), respectively. Choose a reference at infinity when calculating V from E, (V(infinity) = 0), and ignore the effect of the other sphere when doing the calculation for each. The two spheres are now connecting by a conducting wire. From our problem session and handout 6, and the fact that the electric field inside a conductor is zero, we can conclude that the electric potential on the surfaces of the two spheres MUST be equal. Use parts a and b to calculate the ratio of q1 and q2 in terms of r1 and r2. Use parts a,b, to calculate the ratio of the electric fields just outside the surfaces of spheres, in terms of r1 and r2. Draw the electric field lines for the following system:

Answer 1