Question

How you define electrical field generated by infinite long charged road with linear density of charge λ on distance r.

Answer 1

Answer 2

The electric field generated by an infinite long charged rod with a linear charge density λ at a distance r from the rod can be defined using Coulomb's Law. Coulomb's Law describes the electric field (E) at a point due to a point charge, but for an infinite long rod, we can treat it as an approximation of an infinite series of point charges.

Consider a small segment of the rod with a length dl at a distance s from the point where we want to calculate the electric field, as shown in the diagram below:

cssCopy code         dl
  ----------------
       |   s
       |
       | r
       |

The charge dq on this small segment dl is given by: dq = λ * dl

The electric field dE at the point P due to this small segment dl can be calculated using Coulomb's Law: dE = (1 / 4πε₀) * (dq) / (s²)

where ε₀ is the vacuum permittivity (a fundamental constant in electromagnetism).

Since the rod is infinitely long, we need to integrate over the entire length of the rod to find the total electric field at point P. The linear charge density λ is constant along the rod, so the integral becomes:

E = ∫ (1 / 4πε₀) * (λ * dl) / (s²)

Now, the limits of the integral depend on whether we consider the entire rod (from -∞ to +∞) or only a finite segment. For the infinite rod case, we would integrate from -∞ to +∞, but if we are considering only a finite segment, we would integrate over the limits of that segment.

After performing the integration, the result will give the electric field magnitude at distance r due to the infinite long charged rod with linear charge density λ. The direction of the electric field will be radial, pointing away from or toward the rod depending on the sign of λ (positive or negative charge density).