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. $4\pi {\epsilon }_{0}A{a}^3$
• B. ${\epsilon }_{0}A{a}^3$
• C. $4\pi {\epsilon }_{0}A{a}^2$
• D. $A{\epsilon }_0{a}^2$

Answer 1

Answer: (A)

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 ${\varphi }_{net}=\frac{q_{en}}{{\epsilon }_0}$
$\Rightarrow (Aa)\times (4\pi a^2)=\frac{q}{{\epsilon }_0}$ [Using equation (i)]
$\therefore q=4\pi {\epsilon }_{0}A{a}^3$