What is the magnitude of the line charge density on the power line? Express your answer using two significant figures.

 λ = -47 nC / m  

Explanation:

The missing question is as follows:

" The potential difference between the surface of a 2.2 cm -diameter power line and a point 1.9 m distant is 3.8 kV. What is the magnitude of the line charge density on the power line? Express your answer using two significant figures.  "

Given:

- The Diameter of the power line D = 2.2 cm

- The distance between two ends of power line L = 1.9m

- The potential difference across two ends V = 3.8 KV

Find:

What is the magnitude of the line charge density on the power line?

Solution:

- The derivation of the line of charges for a length L oriented along any axis centered at origin and the potential difference between two ends is as follows:

                                      V = 2*k*λ*Ln( D / L )

Where,

k : Coulomb's Constant = 8.99*10^9

 λ : The line charge density

- Re-arrange and solve for λ:

                                     λ = V / 2*k*Ln( D / L )

Plug in the values:

                                    λ = 3800 / 2*8.99*10^9*Ln( 2.2 / 190 )

                                    λ = -4.74022*10^-8 C / m

                                   λ = -47 nC / m