This problem has 2 questions. The 1st is : if ρ=Ar , the relation between E and p. The 2ed is : if I want p=αE , how to solve ρ? Lets solve 2ed question: Assume ρ=B (B is a constant）. ∮E⋅da=E（4πr²）=Q/(ε₀)=∫B4πr²dr/(ε₀) . We can solve： E=Br/3(ε₀)， so r=3(ε₀)E/B, so p=qr=3q(ε₀)E/B， then we can see p is proportional to E. So we can see if ρ=B(the charge density is a constant），p is proportional to E.

This problem has 2 questions.

The 1st is : if ρ=Ar , the relation between E and p.

The 2ed is : if I want p=αE , how to solve ρ?

Lets solve 2ed question:

Assume ρ=B (B is a constant）.

∮E⋅da=E（4πr²）=Q/(ε₀)=∫B4πr²dr/(ε₀) .

We can solve：

E=Br/3(ε₀)，

so r=3(ε₀)E/B,

so p=qr=3q(ε₀)E/B，

then we can see p is proportional to E.

So we can see if ρ=B(the charge density is a constant），p is proportional to E.