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A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 12.5 cm, and the outer sphere has radius 14.8 cm. A potential difference of 120 V is applied to the capacitor. (a) What is the energy density at r = 12.6 cm, just outside the inner sphere? (b) What is the energy density at r = 14.7 cm, just inside the outer sphere? (c) For a parallel-plate capacitor the energy density is uniform in the region between the plates, except near the edges of the plates. Is this also true for a spherical capacitor?

Short Answer

Expert verified

(a)The energy density atr=12.6 just outside the inner sphere is:1.63×10-4J.m-3

(b) The energy density atr=12.6 just outside the inner sphere is8.8×10-5J.m-3

(c) No, the energy density is not uniformly distributed in the region between the plates except the near the edges of the plate.

Step by step solution

01

Calculating the density

Given,

rb=14.8cmra=12.5cmV=120V

Now, to get density we need to find the charge for hollow spheres, and the potential difference between the surface is given by:

Vab=kQ1ra-1rb

Substituting the values, we get:

Q=Vabk1ra-1rb=1209×10910.125-10.148=10.72×10-9C

Now, the density is given by:

u=Q232π2ε0r4

Substituting the values, we get:

u=10.72×10-9232π2×8.85×10-12×0.1264=1.63×10-4J.m-3

Therefore, the density is1.63×10-4J.m-3

02

Energy distribution

We, know that density is given by:

u=10.27×10-9232π2×8.85×10-12×0.1474=8.8×10-5J.m-3

Therefore, we can conclude that the energy density is not uniformly distributed, but decreases while being close to the outer shell.

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