Question

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

• A. $4 \,\pi\varepsilon_0\, Aa^3$
• B. $\varepsilon_0\, Aa^3$
• C. $4 \, \pi\varepsilon_0 \, Aa^2$
• D. $A \, \varepsilon_0 \,a^2$

Answer 1

Answer: (A)

$4 \,\pi\varepsilon_0\, Aa^3$

Answer 2

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)]
$\therefore q = 4\pi\varepsilon _0Aa^3$