According to Gauss law, the electric field of an infinitely long straight wire is proportional to

CONCEPT:

Gauss’s Law: 

• The total electric flux through a closed surface is 1/εo times the charge enclosed in the surface i.e.

\(\Rightarrow {\rm{\Phi }} = \frac{q}{{{\epsilon_o}}}\)

• But we know that Electrical flux through a closed surface is:

\(\Rightarrow \oint \vec E \cdot \overrightarrow {ds} \)

\(\Rightarrow \oint \vec E \cdot \overrightarrow {ds} = \frac{q}{{{\epsilon_o}}}\)

Where, E = electric field, q = charge enclosed in the surface and εo = permittivity of free space.

EXPLANATION:

Electric field due to line charge:

• The electric field due to an infinitely long straight conductor is:

\(\Rightarrow E=\frac{\lambda }{2\pi {{\epsilon }_{o}}r}~\)

Where λ = linear charge density, r = radius of the cylinder, and ε_o = permittivity of free space.

• From the above equation, it is clear that the electric field of an infinitely long straight wire is proportional to 1/r. Hence option 2 is correct.