The electric field in a certain region is acting radially outward and is given by E = Aa. A charge contained in a sphere of radius ’ a ’ centered at the origin of the field, will be given by ?
(a) \( A \varepsilon_0 a^2 \)
(b) \( 4 \pi \varepsilon_0 A a^3 \)
(c) \( \varepsilon_0 A a^3 \)
(d) \( 4 \pi \varepsilon_0 A a^2 \)
Answer : (b) \( 4 \pi \varepsilon_0 A a^3 \)
\( \Phi = A a \)
\( E = \dfrac{1}{4 \pi \varepsilon_0} \cdot \dfrac{q}{a^2} \)
\( A a = \dfrac{1}{4 \pi \varepsilon_0} \cdot \dfrac{q}{a^2} \)
\( q = 4 \pi \varepsilon_0 A a^3 \)
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