A charge q is distributed over the volume of a sphere of radius R. Assuming the permittivty to be equal to unity, compare the energy stored inside the sphere with the energy pervading the surrounding space. [Hint: `u=(1)/(2)epsilon_(0)E^(2).`]
Answered Feb 05, 2023
Correct Answer - `1:5`
Correct Answer - `-(Q^(2))/(16pi in_(0)R)`
Correct Answer - (a). `rho(r)=(Q)/(piR^(4))r` (b) `(Qr_(1)^(2))/(4pi in_(0)R^(4))`
Correct Answer - (a). `Q=2pibR^(2)` (b). `E=(b)/(2epsilon_(0))`
Correct Answer - `(1)/(5)qwr^(2),(q)/(2m)`
Correct Answer - `v=sqrt(1/(4piepsi_0)(2Q^2)/(Rm)`
Correct Answer - `(q^(2))/(8piepsilon_(0)R)`
Correct Answer - 36 kV, 3kV, 6kV
Correct Answer - `2.25q`
Correct Answer - `[(pirho_(0)^(2)R^(5))/(72 in_(0)) , (13pirho_(0)^(2)R^(5))/(630 in_(0))]`
Correct Answer - ` 4500 pi cm^(3)`
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