Let there be a spherically symmetric charge distribution with charge density varying as ρ(r)=ρ₀(5/4-r/R) up to r=R, and ρ(r)=0 for rR, where r is the distance from the origin. The electric field at a distance r (r

Question

Let there be a spherically symmetric charge distribution with charge density varying as ρ(r)=ρ₀(5/4-r/R) up to r=R, and ρ(r)=0 for r>R, where r is the distance from the origin. The electric field at a distance r (r<R) from the origin is given by

Accepted Answer

(3) (ρ₀r)/(4ε₀)(5/3-r/R). Enclosed charge inside radius r: q=∫₀^rρ₀(5/4-(r')/R)4π r'²dr'=4πρ₀[(5r³)/(12)-(r⁴)/(4R)]. Gauss's law: E(4π r²)=q/(ε₀), so the 4π cancels and E=(ρ₀)/(ε₀ r²)[(5r³)/(12)-(r⁴)/(4R)]. E=(ρ₀ r)/(ε₀)[5/(12)-r/(4R)]. Taking 1/4 out of the bracket: E=(ρ₀r)/(4ε₀)(5/3-r/R).

Let there be a spherically symmetric charge distribution with charge density varying as ρ(r)=ρ₀(5/4-r/R) up to r=R, and ρ(r)=0 for r>R, where r is the distance from the origin. The electric field at a distance r (r<R) from the origin is given by

Step-by-step solution

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