The electric field in a certain region is acting radially outward and is given by E = Ar ….

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

(a) A ε0 a2

(b) 4 π ε0 A a3

(c) ε0 A a3

(d) 4 π ε0 A a2

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Ans: (b)
Sol: Electric Flux linked with sphere $\displaystyle = \vec{E}.\vec{S} $

Since electric field is radial. It is always perpendicular to the surface of the sphere.

So ,  φ = E S cos⁡0 = E S

φ = A r (4π r2 )

φ = 4 A π a3 ; (as r=a)

According to Gauss’s law,

φ = q/∈0

or, q = φ ∈0

q = 4 π ∈0 A a3