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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Attached question and diagram.
6. Question 3... Calculate the electric potential energy for the configuration of charges q1, 2 and q3 as shown in the equilateral triangle in Fig.2. у-ахis Fig. 3 93 = +0.66 µC 5.0 cm 5.0 cm A B Х-ахis q1 = +0.70 µC 5.0 сm 92 = +1.2 µC
5. A uniform electric field of magnitude 250 V/m is directed in the positive x direction. A 112.0-µC charge moves from the origin to the point (x, y) = (20.0 cm, 50.0 cm). (a) What is the change in the potential energy of the charge-field system?
4. charge moves a distance of 2.0 cm in the direction of a uniform electric field whose magnitude is 215 N/C. As the charge moves, its electrical potential energy decreases by 6.9 x10-19 J. Find the charge on the moving particle. What is the potential difference between the two locations?
1. Two point charges q1 = +26µC and q2 = −17.5µC are 64 cm apart.a. What is the potential energy of the system of two charges?b. What is the electric potential at a point between them 24 cm from q1?
5. In a certain region of space, potential difference between two points A and B is 50 V (VĄ – Vg = 50 V). What is the work done by the electric field to move a proton from point A to B? [V» = 0] Answer: 80 x 10-19 J 6. Figure shows two charged particles separated by 12 cm. Find the electrostatic potential energy of the system. Q1 = 2 µC Q-3 μC d = 12 cm Answer: -0.45 J
8. Two point charges, q1=q2=13nC, are located on the x-axis and is 8 meters apart. Assuming that q1 is located at the origin: a. Find the work that must be done by an external force to bring a third point charge q3 =-13nC from infinity to x=11m. b. Find the total potential energy of the system of three charges.
4) The electric field in a certain region is given by the expression E = 4x3 i (N / C). What is the potential difference (V2 - V1 ) between the points x1 = 1 m and x2 = 2 m on the x-axis?
34. I need help with these questions. The question reads: A uniform electric field has magnitude 240 N/C and is directed to the right. A particle with charge +4.2 nC moves along the straight line from a to b. a) what is the electric force that acts on the particle? B) what is the work done on the particle by the electric field? C) what is the potential difference Va-Vb between points a and b?
5. Three point-like charges are placed at the corners of a rectangle as shown in the figure, a = 38.0 cm and b = 48.0 cm. q2 = +3.30 μC, Find the work done by the electric field force when the charge q2 is moved to infinity. Let q₁ = -2.50 µC, 93 = +3.60 μC. J f60 ssf60 s too s ai 91 ssf60 ssf60 ssf60 ssf60 ssf60 ssfóð 09js (9) 09.19js (9js (9jss 93 ssf60 ssss$60 ssf60 sst ssf6092 oss is mos f60 ssf60 ssf60 ssf60 ssf60 ssf60 50 ssf60 ssf60 ssf
. Consider the spherical equipotential surfaces of a positive point charge as shown. A positive test charge 90 = 1.00 x 10 'Cis brought from X to Y, and then to Z. What is the total work done by the electric field in moving the test charge? A. Zero B. 1.00 x 10 8 J C. 2.00 x 10 8 J D. -1.00 x 10 8 J
10. You need a coaxial cable that can hold ± 62 nC/m of charge density. Someone hands you a cable with a 2.0 mm diameter inner conductor and 1.6 cm outer conductor (see diagram at right). The maximum potential difference the cable will tolerate is 2 kV. Will this cable work for your application? a-