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Question
A metal sphere of radius R is charged to a potential V.
- Find the electrostatic energy stored in the electric field within a concentric sphere of radius 2 R.
- Show that the electrostatic field energy stored outside the sphere of radius 2 R equals that stored within it.
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Solution
- potential of the inner metallic sphere is given by V = `1/(4pi∈_0) q/R`
capacitance of the capacitor formed by two concentric spheres of radii R and 2R is given by
`C = 4pi∈_0 (R xx 2R)/(2R-R)`
`C = 4pi∈_0 xx 2R`
potential of the outer sphere is given by
`V_2 = 1/(4pi∈_0) q/(2R) = V/2` - Electrostatic energy stored outside the sphere is given by `E = 1/2C(V - V_2)^2`
`E = 1/2 xx 4pi∈_0 xx 2R xx V^2/4`
`E = pi∈_0 xx RV^2`
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