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

Answer 1

The correct option is C $4\pi {\epsilon }_{0}A{a}^3$

Here $r=a$

from equation (1)

$E=\frac{1}{4\pi {\epsilon }_0}.\frac{q}{a^2}=Aa$

$q=4\pi {\epsilon }_{0}A{a}^3$