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The electric field in a region is radial...

The electric field in a region is radially outward with magnitude `E=Ar`. Find the charge contained in a sphere of radius a centred at the origin. Take `A=100 V m^(-2)` and `a=20.0 cm`.

Text Solution

Verified by Experts

The correct Answer is:
`3 xx 10^(-10) C`
Consider a spherical shell of radius x. The electric flux through
this surface is
`phi = int vecE * dvecS = E_r4pir^2`
Therefore, the electric flux through spherical suface of radius
R will be
`phi = int vecE * d vecS = E_r 4pir^2`
When `r = R, E_R = alphaR`, we have `phi = alphaR4piR^2`
By Gauss theorem, net electric flux is
`1/epsilon_0 xx` change enclosed
:. `alpha R4piR^2 = 1/epsilon_0 Q_(encl osed)` or `Q_(enclosed) = (4piepsilon_0)alphaR^3`
Given `R = 0.30m, alpha = 100 Vm^(-2)`
`Q_(en clo sed) = 1/(9 xx 10^(9)) xx 100 xx (0.30)^3 = 3 xx 10^(-10)C`.
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