If the linear charge density of an infinitely long straight uniformly charged wire is λ, then the force on the charge q present at a distance r from the wire is:

CONCEPT:

Electric field intensity: 

• It is defined as the force experienced by a unit positive test charge in the electric field at any point.

\(⇒ E=\frac{F}{q_{o}}\)    

Where E = electric field intensity, qo = charge on the particle

Electric field intensity due to an infinitely long straight uniformly charged wire:

• The direction of the electric field at every point must be radial (outward if λ > 0, inward if λ < 0).

\(⇒ E=\frac{λ}{2\piϵ_or}\)

Where λ = linear charge density, ϵo = permittivity, and r = distance of the point from the wire

EXPLANATION:

• We know that the electric field intensity due to an infinitely long straight uniformly charged wire is given as,

\(⇒ E=\frac{λ}{2\piϵ_or}\)    -----(1)

Where λ = linear charge density, ϵo = permittivity, and r = distance of the point from the wire

• The magnitude of electric force experienced by a charged particle q in an electric field E is given as,

⇒ F = Eq    -----(2)

By equation 1 and equation 2, the force on the charge q present at a distance r from the wire is given as,

⇒ F = Eq

\(⇒ F=\frac{λq}{2\piϵ_or}\)

• Hence, option 1 is correct.