If an insulated non-conducting sphere of radius R has charge density ρ . The electric field at a distance r from the centre of sphere (r R) will be:

Question

If an insulated non-conducting sphere of radius R has charge density ρ . The electric field at a distance r from the centre of sphere (r > R) will be: (A) (ρ R/3 ε0) (B) (ρ r/ε0) (C) (ρ r/3 ε0) (D) (3 ρ R/ε0)

Tardigrade Admin · Accepted Answer

Charge which is enclosed in the surface is given by σ=(4/3) π r3 ρ Now according to Gaussian law ε φ E d s=σ, ε0 E 4 π r2=(4/3) π r3 ρ E=(ρ r/3 ε0)

Q. If an insulated non-conducting sphere of radius $R$ has charge density $ρ .$ The electric field at a distance r from the centre of sphere $(r > R)$ will be:

$\frac{ρR}{3 ε _{0}}$

$\frac{ρ r}{ε _{0}}$

$\frac{ρ r}{3 ε _{0}}$

$\frac{3 ρR}{ε _{0}}$

Charge which is enclosed in the surface is given by
$σ = \frac{4}{3} π r^{3} ρ$
Now according to Gaussian law
$ε ϕ E d s = σ,$
$ε_{0} E 4 π r^{2} = \frac{4}{3} π r^{3} ρ$
$E = \frac{ρ r}{3 ε _{0}}$

Q. If an insulated non-conducting sphere of radius R has charge density ρ. The electric field at a distance r from the centre of sphere (r>R) will be:

3ε0​ρR​

ε0​ρr​

3ε0​ρr​

ε0​3ρR​