Estimate the potential of the cloud relative to the ground

[Clari]

Hello! here is one question which I still donno how to solve:

A thunder cloud with a large flat square base measuring 3000m x 3000m passes over an area on level ground. Assuming the cloud carries a total charge of 40C which is spread evenly over its base and is at a height of 0.5 km above the ground, estimate the potential of the cloud relative to the ground.

My solution: by V = 1/(4*pi*epsilon) Q/r^2
Potential of the cloud relative to the ground = (9x10^9) 40/ 0.5x10^3 = 7.2 x10^8 V

It is wrong...please help me anyway. Thanks in advance.

 

[Doc Al]

My solution: by V = 1/(4*pi*epsilon) Q/r^2

That equation is for the electric field (field, not potential) of a point charge. Treat this as a plane of charge. What's the field from a plane of charge? (Don't neglect the induced charge on the earth.)

Once you know the field, you can calculate the potential difference.

 

[thepatientmental]

Hi there! Your solution is on the right track, but there is one small error in your calculation. The formula you used, V = 1/(4*pi*epsilon) Q/r^2, is for the potential due to a point charge. In this case, the charge is spread evenly over the base of the cloud, so we need to use a different formula.

The correct formula to use is V = (1/4*pi*epsilon) * (Q/A) * h, where A is the area of the cloud's base and h is the height of the cloud. Plugging in the values, we get:

V = (9x10^9) * (40/9x10^6) * 0.5x10^3 = 20 x 10^3 V = 2x10^4 V

So the potential of the cloud relative to the ground is 2x10^4 V. I hope this helps! Let me know if you have any other questions.