Two spherical conductors of radii r 1 and r 2 are separated by a distance much g

Question

Two spherical conductors of radii r1 and r2 are separated by a distance much greater than the radius of either sphere. The spheres are connected by a conducting wire as shown in the figure. The charges on the spheres in equilibrium are q1 and q2, respectively, and they are uniformly charged. Find the ratio of the magnitudes of the electric fields at the surfaces of the spheres.

What if initially a charge 2.1 C is put on shell #1 with radius 3.4 m, then a far away shell #2 (initially neutral) with radius 8.3 m is connected to shell #1 by a long conducting wire.
(a) What is the final charge on shell #1?
Q = ........... C


(b) What is the final charge on shell #2?
Q = ................. C

(c) What is the electric potential V on shell #1?
V = ................... V

(d) What is the electric potential V on shell #2?
V = ....................... V

Explanation / Answer

We have: q1 + q2 = q0 (conservation of charges) and: q1/r1 = q2/r2 (same electric potential) q1+q2 = 2.1 .........................1 and q1/3.4 = q2/8.3 .........................2 q1 = 0.409*q2 substituiting in eqn 1 gives 1.409*q2 = 2.1 q2 =1.49 C which gives q1 = 2.1 - 1.49 = 0.61 C c) electric potential is k*q/r for a shell you can calculate this..

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