Let there be a spherical symmetric charge distribution with charge density varying as p(r)=p0(r/R) upto r=R and ρ (r)=0 for rR, where r is the distance from the origin. The electric field at on a distance r (r

Question

Let there be a spherical symmetric charge distribution with charge density varying as p(r)=p0(r/R) upto r=R and ρ (r)=0 for r>R, where r is the distance from the origin. The electric field at on a distance r (r < R) from the origin is given by - (A) (ρ 0 r2/4 ϵ 0 R) (B) (ρ 0 r/4 ϵ 0 R) (C) (ρ 0 r4/ϵ 0) (D) (ρ 0 r2/ϵ 0 R)

Tardigrade Admin · Accepted Answer

oint overset arrow E â. overset arrow d s=(qi n/ϵ 0) ....(1) Solution

qi nqi n =â«0rÏ4Ïr2dr=â«0rÏ0rR4Ïr2dr=4ÏÏ0Rr44 =(π ρ 0 r4/R) , from (1) E.4π r2 =(π ρ 0 r4/ϵ 0 R) ∴ E =(ρ 0 r2/4 ϵ 0 R)

Q. Let there be a spherical symmetric charge distribution with charge density varying as $p (r) = p_{0} \frac{r}{R}$ upto $r = R$ and $ρ (r) = 0$ for $r > R,$ where r is the distance from the origin. The electric field at on a distance $r (r < R)$ from the origin is given by -

$\frac{ρ _{0} r ^{2}}{4 ϵ _{0} R}$

$\frac{ρ _{0} r}{4 ϵ _{0} R}$

$\frac{ρ _{0} r ^{4}}{ϵ _{0}}$

$\frac{ρ _{0} r ^{2}}{ϵ _{0} R}$

$\oint E \to ‍. d s \to = \frac{q _{in}}{ϵ _{0}}$ ....(1)

$q_{in} q_{in}$ =∫0rρ4πr2dr=∫0rρ0rR4πr2dr=4πρ0Rr44
$= \frac{π ρ _{0} r ^{4}}{R}$ , from (1)
$E .4 π r^{2} = \frac{π ρ _{0} r ^{4}}{ϵ _{0} R} ∴ E = \frac{ρ _{0} r ^{2}}{4 ϵ _{0} R}$

Q. Let there be a spherical symmetric charge distribution with charge density varying as p(r)=p0​Rr​ upto r=R and ρ(r)=0 for r>R, where r is the distance from the origin. The electric field at on a distance r(r<R) from the origin is given by -

4ϵ0​Rρ0​r2​

4ϵ0​Rρ0​r​

ϵ0​ρ0​r4​

ϵ0​Rρ0​r2​