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Question:

Electric field outside a long wire carrying charge q is proportional to:

1r13/2

1r

1r13/5

1r2

Solution:

Using Gauss Law across the cylindrical Gaussian surface, ∫E.dS=qenc/ε0
∴E × 2πr × l = λ × l/ε0
∴E = λ/2πrε0
Here λ is the linear charge density on the wire.