The charge per unit length on a long, straight filament is 290.0 mC/m. Find the electric field a) 10.0 cm andb) 100 cm from the filament, where distances are measured perpendicular to the length of the filament.

Explanation:

given linear charge density λ = 290 x 10⁻³ C / m

Expression for electric field at distance d is given as follow .

E = λ / 2πε₀r

1 / 4πε₀ = 9 x 10⁹

1 / 2πε₀ = 18 x 10⁹

E = λ / 2πε₀r = 290 x 10⁻³ x 18 x 10⁹ / r

= 5220 x 10⁶ / r

For r = 10 x 10⁻² m = .1 m

E = 5220 x 10⁶ / .1

= 5.22 x 10¹⁰ N/m

For r = 100 x 10⁻² m = 1 m

E = 5220 x 10⁶ / 1

= 5.22 x 10⁹ N/m .