Confirming my logic on potential difference

[The Blind Watchmaker]

Homework Statement

You’ve decided to protect your house by placing a 5.0 m tall iron lightning rod next to the house. The top is sharpened to a point and the bottom is in good contact with the ground. From your research, you’ve learned that lightning bolts can carry up to 50 kA of current and last up to 50μs. You don’t want the potential difference between the top and bottom of the lighting rod to exceed 100 V. What minimum diameter must the rod have? Conductivity of iron is 1.0 x [10][/7] [(Ωm)][/-1]

Homework Equations

V = IR
R = ρ L/A
ΔV = [V][/b] - [V][/a]

The Attempt at a Solution

ΔV = [V][/b] - [V][/a]
Assume [V][/a] to be 0
[V][/b] = ΔV
IR = ΔV
I ρ L/A = ΔV
I L/(σA) = ΔV
50⋅[10][/3]⋅5/([10][/7]⋅π[r][/2]) = 100
r = 0.892 cm
d = 2r = 1.8 cm

Can someone check my working to verify my logic?
P.S: I have no background in physics as I was a Biology olympiad medalist but I am currently taking an Electromagnetism module as part of my course requirement. Any help would be appreciated! :)

 

[gneill]

Hi The Blind Watchmaker,



Your calculations and result look fine.

Note that you can insert subscripts and superscripts easily using the $x_2$ and $x^2$ icons from the edit window toolbar (Or use LaTeX syntax as I did for x₂ and x² )

 

[The Blind Watchmaker]

Thank you! This is my first post so I am not really familiar with the syntax yet.