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

Question

The electric field in a certain region is acting radially outward and is given by E= Ar. The charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by : (A) A ε0 a2 (B) 4 π ε0 Aa 3 (C) ε0 Aa 3 (D) 4 π ε0 Aa 2

Tardigrade Admin · Accepted Answer

E=A vecr=A r hatr text Area =4 π r2 hatn ⇒ φ= vecE ⋅ text Area =A a × 4 π a2 also φ(r=a)=4 π Aa 3 So, q text in =φ ⋅ ε0=4 π a3 A ∈0

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

$A ε_{0} a^{2}$

$4 π ε_{0} A a^{3}$

$ε_{0} A a^{3}$

$4 π ε_{0} A a^{2}$

$E = A r = A r \overset{r}{^}$
$Area = 4 π r^{2} \overset{n}{^}$
$\Rightarrow ϕ = E \cdot Area = A a \times 4 π a^{2}$
also $ϕ_{(r = a)} = 4 π A a^{3}$
So, $q_{in} = ϕ \cdot ε_{0} = 4 π a^{3} A \in_{0}$

Q. The electric field in a certain region is acting radially outward and is given by E= Ar. The charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by :

Aε0​a2

4πε0​Aa3

ε0​Aa3

4πε0​Aa2