Question

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

• A. $4 \pi \varepsilon_{0} A a^{2}$
• B. $A \varepsilon_{0} a^{2}$
• C. $4 \pi \varepsilon_{0} Aa ^{3}$
• D. $\varepsilon_{0} A a^{3}$

Answer 1

Answer: (C)

Given,
$E=A r\,\,\,...(i)$

Here, $ r=a $
$\Rightarrow E=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q}{a^{2}}$
From Eq. (i), we get
$\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q}{a^{2}}=A a $
$ \Rightarrow q=4 \pi \varepsilon_{0} A a^{3}$