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AN isolated conducting sphere whose radi...

AN isolated conducting sphere whose radius R is 6.85 cm has a charge q=1.25 nC
(a) How much potential energy is stored in the electric field of this charged conductor?
(b) What is the energy density at the surface of the sphere?

Text Solution

Verified by Experts

Substituting `C=4 pi epsilon_0R` into to Eq.25-21 gives us
`U=q^2/(2C)=q^2/(8pi epsilon_0R)`
`=((1.25 times 10^-9 C)^2)/((8pi)(8.85 times 10^-12 F//m)(0.0685 m))`
`=1.03 times 10^-7 J=103 nJ` ,
(b) Here we must first find E at the surface of the sphere, as given by Eq.23-15,
`E=1/(4pie_0) q/R^2`
The energy density is then
`u=1/2 epsilon_0 E^2=q^2/(32 pi^2 epsilon_0 R^4)`
`=((1.25 times 10^-9 C)^2)/((32 pi^2)(8.85 times 10^-12 C^2//N.m^2)(0.0685 m)^4)`
`=2.4 times 10^- J//m^3=25.4 mu J//m^3`
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