Electric field at a point of distance r from a uniformly charged wire ...
Explanation:
The electric field at a point P, which is at a distance r from an infinitely long uniformly charged wire, can be calculated using Coulomb's law. The charged wire has a linear charge density λ, which is the charge per unit length.
Formula: E = (λ / 2πε₀r)
Where,
E = Electric field at point P
λ = Linear charge density of the wire
r = Distance of point P from the wire
ε₀ = Permittivity of free space
Proportional to:
The electric field at a point P from an infinitely long uniformly charged wire is directly proportional to 1/r. This means that as the distance of the point P from the wire increases, the electric field decreases and vice versa.
Explanation:
When the distance of the point P from the wire is doubled, the electric field at that point becomes half of its initial value. This is because the electric field decreases with the square of the distance from the wire. Hence, when the distance is doubled, the electric field becomes 1/4th of its initial value.
Formula: E ∝ 1/r
Where,
∝ = Proportional to
Conclusion:
Hence, we can conclude that the electric field at a point of distance r from a uniformly charged wire of infinite length having linear charge density is directly proportional to 1/r.
Electric field at a point of distance r from a uniformly charged wire ...
E= (lambda)/2.π.(epsilon).r
Thus it is directly proportional to 1/r.
(A)
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