Consider the magnitude of electric field E at a point at distance r due to an infinitely long straight wire charged with a uniform charge density λ. Then for a given λ.

Concept:

Electric field:

• ​It is defined as the force per unit of positive charge.
• Formula, Electric field, \(E=\frac{F}{q}\) where F = force,  q = positive charge
• The SI unit of electric charge is N/C.

Electric field due to an infinitely long straight wire:

•  Consider an infinitely long straight, uniformly charged wire. Let the linear charge density of this wire be λ. P is the point that is located at a perpendicular distance from the wire. The distance between point P and the wire is r.

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• The electric field is due to an infinitely long straight wire, \(E =\frac{\lambda}{2\pi \epsilon_0 r}\).

Explanation:

The magnitude of electric field E at a point at distance r due to an infinitely long straight wire charged with a uniform charge density λ is given by,

\(E =\frac{\lambda}{2\pi \epsilon_0 r}\)

From the above expression, the magnitude of the electric field due to an infinitely long straight wire is inversely proportional to the distance at which the electric field is calculated.

So, \(E\propto \frac{1}{r}\)

Hence, the correct option is 2.