A very long, straight wire has charge per unit length 3.50*10^-10 C/m. At what distance from the wire is the electricfield magnitude equal to 2.90 N/C?

r = 2.17 m

Explanation:

Conceptual Analysis:

The electric field at a distance r from a charge line of infinite length and constant charge per unit length is calculated as follows:

E = 2k * (λ/r) Formula (1)

Where:

E: electric field. (N/C)

k: Coulomb electric constant. (N*m²/C²)

λ: linear charge density. (C/m)

r : distance from the charge line to the surface where E calculates (m)

Known data

E = 2.9 N/C

λ = 3.5*10⁻¹⁰ C/m

k = 8.99 * 10⁹ N*m²/C²

Problem development

We replace data in the formula (1):

E = 2*k * (λ/r)

2.9 = 2*8.99 * 10⁹ * (3.5*10⁻¹⁰/r)

r = (2*8.99 * 10⁹*3.5*10⁻¹⁰) / (2.9)

r = 2.17 m