A long solid non-conducting cylinder of radius R is charged such that the volume charge density is proportional to r where r is the distance from axis. The electric field E at a distance r ( r

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A long solid non-conducting cylinder of radius R is charged such that the volume charge density is proportional to r where r is the distance from axis. The electric field E at a distance r ( r < R ) will depend on r as

TestHub · Accepted Answer

​ ( b ) : ρ ∝ r ; ρ = Kr d Q = ρ V = Kr ( 2 π r d r ) × l ​ Using Gauss's Law, ​ E .2 π r l = ε 0 ​ ∫ 0 r ​ Kr .2 π r l . d r ​ ⇒ E = K 3 ε 0 ​ r 2 ​ ∴ E ∝ r 2 ​

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