Answer:
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
