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1. Electric Charges and Fields
hard
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
$4\pi {\varepsilon _0}A{a^2}$
B
$A$${\varepsilon _0}{a^2}$
C
$\;4\pi {\varepsilon _0}A{a^3}$
D
$\;{\varepsilon _0}A{a^2}$
(AIPMT-2015)
Solution
According to question, electric field varies as
$E=A r$
Here $r$ is the radial distance.
At $r=a, E=A a………(i)$
Net flux emitted from a spherical surface of radius $a$ is $\phi_{\mathrm{net}}=\frac{q_{e n}}{\varepsilon_{0}}$
$\Rightarrow \quad(A a) \times\left(4 \pi a^{2}\right)=\frac{q}{\varepsilon_{0}} \quad[\text { Using equation }(\mathrm{i})]$
$\therefore \quad q=4 \pi \varepsilon_{0} A a^{3}$
Standard 12
Physics
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