Capacitance and maximum charge HELP

[seant]

As a crude model for lightning, consider the ground to be one plate of a parallel-plate capacitor and a cloud at an altitude of 620 m to be the other plate. Assume the surface area of the cloud to be the same as the area of a square that is 0.40 km on a side.
(a) What is the capacitance of this capacitor?
nF
(b) How much charge can the cloud hold before the dielectric strength of the air is exceeded and a spark (lightning) results?
C

I used C=E0 A/D (8.85*10^-12 C^2/N*m^2)(.16km^2/620m) and conversions also, but to no avail can someone please help

 

[alphysicist]

Hi seant,

As a crude model for lightning, consider the ground to be one plate of a parallel-plate capacitor and a cloud at an altitude of 620 m to be the other plate. Assume the surface area of the cloud to be the same as the area of a square that is 0.40 km on a side.
(a) What is the capacitance of this capacitor?
nF
(b) How much charge can the cloud hold before the dielectric strength of the air is exceeded and a spark (lightning) results?
C

I used C=E0 A/D (8.85*10^-12 C^2/N*m^2)(.16km^2/620m) and conversions also, but to no avail can someone please help

What number did you get as your final answer, in nF?

 

[baba89]

I can understand your confusion and frustration. Capacitance is a complex concept and calculating it in real-life scenarios can be challenging. Let me try to break it down for you.

Firstly, let's understand what capacitance is. It is a measure of a capacitor's ability to store electrical charge. In this case, the ground and the cloud are acting as two plates of a parallel-plate capacitor. The capacitance of a parallel-plate capacitor is given by the formula C = ε0A/d, where ε0 is the permittivity of free space, A is the area of the plates, and d is the distance between the plates.

Now, let's apply this formula to our scenario. The permittivity of free space, ε0, is a constant value of 8.85*10^-12 C^2/N*m^2. The area of the cloud can be calculated by taking the square of its side, which is 0.40 km. This gives us an area of 0.16 km^2. Finally, the distance between the ground and the cloud is 620 m.

Putting these values into the formula, we get C = (8.85*10^-12 C^2/N*m^2)(0.16 km^2/620 m) = 2.28 nF. So, the capacitance of this capacitor is 2.28 nanofarads.

Now, to calculate the maximum charge the cloud can hold, we need to use another formula, Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. In this case, the maximum voltage is the dielectric strength of air, which is approximately 3 million volts per meter.

Putting these values into the formula, we get Q = (2.28*10^-9 F)(3*10^6 V/m) = 6.84*10^-3 C. So, the cloud can hold a maximum charge of 6.84 milliCoulombs before the dielectric strength of air is exceeded and a spark (lightning) occurs.

I hope this explanation helps you understand the concept of capacitance and how to calculate it in a real-life scenario. Please feel free to ask any further questions if you have any doubts.