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Q.

The electric intensity due to an infinite cylinder of radius R and  having charge q per unit length at a distance r(r>R) from its axis is

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a

Directly proportional to r2

b

Directly proportional to r3

c

Inversely proportional to r

d

Inversely proportional to r2

answer is C.

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Detailed Solution

According to Gauss law ∮E ⋅ ds==qlε0∮ds=2π rl; (E is constant)∴ E⋅2πrl=qlε0⇒E=q2πε0r i.e. E∝1r
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The electric intensity due to an infinite cylinder of radius R and  having charge q per unit length at a distance r(r>R) from its axis is