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  4. The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by

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Q. The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by

AIPMTAIPMT 2015Electrostatic Potential and Capacitance

Solution:

According to question, electric field varies as
E = Ar
Here r is the radial distance.
At r = a, E = Aa ...(i)
Net flux emitted from a spherical surface of radius a is $ \phi_{net} = \frac{q_{en}}{\varepsilon _0} $
$ \Rightarrow (Aa) \times (4\pi a^2) = \frac{q}{\varepsilon _0}$ [Using equation (i)]
$ \therefore q = 4\pi\varepsilon _0Aa^3 $

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