Question

If a = 7 × 10 ⁻⁶ C/m and b = 1 m, find E at r = 0.6 m⁴. The permittivity of a vacuum is 8.8542 × 10 ⁻¹² C² /N · m² .

Answer 1

To calculate the electric field (E) at 0.6 m from a uniformly charged line with charge density of 7 × 10⁻⁶ C/m, use the expression E = (1/(2πε₀)) * (λ/r), substituting the given values and permittivity of free space.

Step-by-step explanation:

The student has asked for the electric field (E) at a distance of r = 0.6 m from a uniformly charged line with linear charge density a = 7 × 10⁻⁶ C/m. This is a classic physics problem involving the use of Coulomb's Law and the concept of electric field due to a continuous charge distribution. The permittivity of free space (ε₀) is given as 8.8542 × 10⁻¹² C²/N · m².

The general expression for the electric field (E) at a distance r from an infinitely long straight wire with uniform linear charge density λ, in a vacuum, is given by:

E = (1 / (2πε₀)) * (λ / r)

Substituting the given values:

E = (1 / (2π * 8.8542 × 10⁻¹² C²/N · m²)) * (7 × 10⁻⁶ C/m / 0.6 m)

Calculating the above expression will yield the magnitude of the electric field at the specified distance from the charged line.