If electric field in a region is radially outward with magnitude E = Ar, the charge contained in a sphere of radius r centred at the origin is

Question

If electric field in a region is radially outward with magnitude E = Ar, the charge contained in a sphere of radius r centred at the origin is (A) (1/4 π ε0) Ar 3 (B) 4 π ε0 Ar 3 (C) (1/4 π ε0) ( A / r 3) (D) (4 π ε0 A / r 3)

Tardigrade Admin · Accepted Answer

E=(q/4 π ε0 r2) ⇒ A r=(q/4 π ϵ0 r2) ⇒ q=4 π ε0 A r3

Q. If electric field in a region is radially outward with magnitude $E = A r$ , the charge contained in a sphere of radius $r$ centred at the origin is

$\frac{1}{4 π ε _{0}} A r^{3}$

$4 π ε_{0} A r^{3}$

$\frac{1}{4 π ε _{0}} \frac{A}{r ^{3}}$

$\frac{4 π ε _{0} A}{r ^{3}}$

$E = \frac{q}{4 π ε _{0} r ^{2}}$
$\Rightarrow A r = \frac{q}{4 π ϵ _{0} r ^{2}}$
$\Rightarrow q = 4 π ε_{0} A r^{3}$

Q. If electric field in a region is radially outward with magnitude E=Ar, the charge contained in a sphere of radius r centred at the origin is

4πε0​1​Ar3

4πε0​Ar3

4πε0​1​r3A​

r34πε0​A​