An infinitly long wire is charged uniformly with charge density λ and placed in air, the electric field at distance r from wire will be:

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:

Assuming the wire is infinitely long, the electric field will be radial and will have a magnitude given by:

E = \(\frac{\lambda}{2\pi \varepsilon_0r} \)

where

λ is the linear charge density of the wire,

ε₀ is the permittivity of free space, 

r is the distance from the wire.

• The direction of the electric field will be radial and pointing away from the wire if the charge on the wire is positive and towards the wire if the charge on the wire is negative.
• Note that the above formula assumes that the wire is thin compared to the distance from it, and that the electric field is being measured at a point far away from the ends of the wire. If these assumptions are not satisfied, the electric field may be different.