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.

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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