Electric Energy in Space
A static, uniform sphere of electric charge has a radius of meter and a charge of Coulomb. How many Giga-Joules of energy are stored in the electric field in the free space outside the sphere?
Details and Assumptions:
- Permittivity of free space:
-
The answer is 4.494.
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1 solution
The capacitance of a sphere of raduis r is C = 4 π ε 0 r . This can be easily seen by comparing V = Q / C (the expression of the voltage in terms of charge for a capacitor) to V = 4 π ε 0 r Q (the expression for the Coulomb potential of a sphere). The energy stored in the space around the sphere is E = 2 1 C Q 2 = 4 . 4 9 4 G J . There is also a huge potential (voltage) on the sphere, 8.99GV. The electric field on the surface of the sphere is similarly huge, 8.99GV/m.
In real life only a few MV voltage can be reached before sparks begin to fly. Supercharging a van de Graaff generator is a good example of what happens if the voltage is too high.