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

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 π ε0 A a2 (B) A ε0 a2 (C) 4 π ε0 Aa 3 (D) ε0 A a3

Tardigrade Admin · Accepted Answer

Given, E=A r ...(i) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/27d305ca78faca12e6982a0e8892d1d8-.png" /> Here, r=a ⇒ E=(1/4 π ε0) ⋅ (q/a2) From Eq. (i), we get (1/4 π ε0) ⋅ (q/a2)=A a ⇒ q=4 π ε0 A a3

Q. 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

$4 π ε_{0} A a^{2}$

$A ε_{0} a^{2}$

$4 π ε_{0} A a^{3}$

$ε_{0} A a^{3}$

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

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

Q. 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

4πε0​Aa2

Aε0​a2

4πε0​Aa3

ε0​Aa3