Question

An infinite line of charge produces a field of magnitude 6.6 x 10^4 N/C at a distance of 1.9 m. Calculate the linear charge density.

Answer 1

λ = 6.97 *10⁻⁶ C/m

Step-by-step 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= 6.6 x 10⁴ N/C

r = 1.9 m

k= 8.99 *10⁹ N*m²/C²

Problem development

We replace data in the formula (1):

E= 2k*(λ/r)

6.6*10⁴ = 2*(8.99 *10⁹)*(λ/1.9)

(6.6*10⁴)*(1.9) = 2*(8.99 *10⁹) *λ

(12.54* 10⁴) / (17.98*10⁹) = λ

λ = 6.97 *10⁻⁶ C/m