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Bridging Problem: Electric-Field Energy and Capacitance of a Conducting Sphere A solid conducting sphere of radius R carries a charge Q. Calculate the electric-field energy density at a point a distance from the center of the sphere for (a) R. (c) Calculate the total electric field energy associated with the charged sphere. (d) How much work is required to assemble the charge Q on the sphere? (e) Use the result of part (c) to find the capacitance of the sphere. (You can think of the second conductor as a hollow conducting shell of infinite radius.) (Figure 1) Where is the electric-field energy density greatest? Where is it least? Rank locations from strongest to weakest energy density. To rank locations as equivalent, overlap them. View Available Hint(s) Reset Help == ? F>ROSr< -> Greater Less Figure < 1 of 1 > The correct ranking cannot be determined. Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining



Answer :

We know that capacitance due to spherical body having radius R will be C=4πEoR Now when solid sphere replaced by hollow conducing sphere the change will remain on the surface of same radius and hence:

The ability of a material object or device to store electric charge is referred to as capacitance.

1-use result is not affected as radius is same

at infinity V=KQ/r=KQ/∞=0

and potential due to charge sphere on the surface = kq/r  Where k-9×10² Na²/c

Delta V=V(∞)-V®=0-kq/R

Delta v = q/4πEoR

for a sold conducting sphere, there is no electric

field inside the sphere. Hence the electric fielding!

(YXR) is zero.10 ,for r>R, U = 1/2 EoE², E=1/4πEoR  Q/l^2 , U=1/2 Eo 1/(4πEoR )^2 Q^2/r^4

U(r<R),u(r>R)= o,1/2Eo(1/4πEoR)^2 (Q^2/r^4)

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