Question

Two hollow metal spheres are concentric with each other. Theinner sphere has a radius of 0.131 m and a potential of 89.6 V. Theradius of the outer sphere is 0.155 m and its potential is 78.3 V.If the region between the spheres is filled with Teflon, find theelectric energy contained in this space.

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asked 2021-02-18
Two hollow metal spheres are concentric with each other. Theinner sphere has a radius of 0.131 m and a potential of 89.6 V. Theradius of the outer sphere is 0.155 m and its potential is 78.3 V.If the region between the spheres is filled with Teflon, find theelectric energy contained in this space.

Answers (1)

2021-02-20
Electric Energy stored in the sphere \(\displaystyle{E}={\left({\frac{{{1}}}{{{2}}}}\right)}{C}{V}^{{2}}\)
where \(\displaystyle{C}={4}\pi\epsilon_{{0}}{r}\)
for this problem for the first sphere \(\displaystyle{E}_{{1}}={\frac{{{1}}}{{{2}}}}{C}_{{1}}{{V}_{{1}}^{{2}}}\)
\(\displaystyle{C}_{{1}}={4}\pi\epsilon_{{0}}{r}_{{1}}\)
\(\displaystyle{E}_{{1}}={\frac{{{1}}}{{{2}}}}{4}\pi\epsilon_{{0}}{\left({0.131}{m}\right)}{\left({89.6}{V}\right)}^{{2}}\)
\(\displaystyle={\left({0.5}\right)}{\left({4}\cdot{3.14}\cdot{8.85}\cdot{10}^{{-{12}}}\right)}{\left({0.131}{m}\right)}{\left({89.6}{V}\right)}^{{2}}\)
for this problem forthe second sphere \(\displaystyle{E}_{{2}}={\frac{{{1}}}{{{2}}}}{C}_{{2}}{{V}_{{2}}^{{2}}}\)
\(\displaystyle{C}_{{2}}={4}\pi\epsilon_{{0}}{r}^{{2}}\)
\(\displaystyle{E}_{{2}}={\frac{{{1}}}{{{2}}}}{\left({4}\pi\epsilon_{{0}}\right)}{\left({0.155}{m}\right)}{\left({89.6}{V}\right)}^{{2}}\)
\(\displaystyle={\left({0.5}\right)}{\left({4}\cdot{3.14}\cdot{8.85}\cdot{10}^{{-{12}}}\right)}{\left({0.155}{m}\right)}{\left({78.3}{V}\right)}^{{2}}\)
the electric energy contained in this space E=E1-E2
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