I need help with this problem as soon as possible. Consider two charged conducti
ID: 1341833 • Letter: I
Question
I need help with this problem as soon as possible.
Consider two charged conducting spheres, radii r_1 and r_2, with charges q_1 and q_2, 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(r_1) and V(r_2) just on the surface of each sphere as a function of (q_1, r_1) and (q_2, r_2), 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 q_1 and q_2 in terms of r_1 and r_2. Use parts a, b, to calculate the ratio of the electric fields just outside the surfaces of spheres, in terms of r_1 and r_2.Explanation / Answer
We know that the electric field and the electric potential are related as: E = - (Partial derivative of V with respect to r)
This implies V(r1) = - (Integral of E(r1).dr1) [the limits of the integral being from infinity to r1]
hence, V(r1) = kq1/r1
Similarly, V(r2) = kq2/r2
b.) Now for the same potential, we equate the above two expressions to get
q1/q2 = r2 / r1
c.} Again, E(r1) / E(r2) = (q1/r1^2) / (q2/r2^2);
Hence the required ratio, using the relation from (b.) above, is: r2^3 / r1^3