4. Consider two conducting spheres with radii R, and R2 separated by a distance much greater than either radius. A total charge Q is shared between the spheres. We wish to show that when the electric potential energy of the system has a minimum value, the potential difference between the spheres is zero. The total charge Q is equal to q, + 92, where q, represents the charge on the first sphere and q2 the charge on the second. Because the spheres are very far apart, you can assume the charge of each is uniformly distributed over its surface. (a) Show that the energy associated with a single conducting sphere of radius R and charge Q surrounded by a vacuum is Ug = k.q²/2R . (b) Find the total energy of the system of two spheres in terms of q1, the total charge Q, and the radii R, and R2. (c) To minimize the energy, differentiate the result to part (b) with respect to q, and set the derivative equal to zero. Solve for q, in terms of Q and the radii.

4. Consider two conducting spheres with radii R, and R2 separated by a distance much greater than either radius. A total charge Q is shared between the spheres. We wish to show that when the electric potential energy of the system has a minimum value, the potential difference between the spheres is zero. The total charge Q is equal to q, + 92, where q, represents the charge on the first sphere and q2 the charge on the second. Because the spheres are very far apart, you can assume the charge of each is uniformly distributed over its surface. (a) Show that the energy associated with a single conducting sphere of radius R and charge Q surrounded by a vacuum is Ug = k.q²/2R . (b) Find the total energy of the system of two spheres in terms of q1, the total charge Q, and the radii R, and R2. (c) To minimize the energy, differentiate the result to part (b) with respect to q, and set the derivative equal to zero. Solve for q, in terms of Q and the radii.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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