Capacitance of a landing plane in a thunderstorm

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AI Thread Summary
The discussion centers on calculating the capacitance of an airplane's wings acting as a parallel plate capacitor when it acquires a charge of 1 microcoulomb while flying through a thundercloud. To find capacitance, the relevant formula C= |Q/V| is mentioned, but the user struggles with determining the area of the wings and the distance to the ground, which are necessary for calculations. It's suggested to make reasonable assumptions or research specific airplane specifications to obtain these values. Additionally, understanding the potential of the plane and the implications for safety during landing in thunderstorms is emphasized. Proper precautions are necessary to mitigate risks associated with excess charge accumulation.
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Homework Statement



An airplane flies through a thundercloud and picks up an excess charge of 1 microcoulomb. When the plane comes into land, its wings form approximately a parallel plate capacitor with the ground. What is the capacitance of this system?
What is the potential of the plane?
Why does this matter and what precautions are taken to avoid this?

Homework Equations


C= |Q/V|
V= -Ed (E being determined from Gauss' law)
I would insert the other equations but I'm just learning how to use this system and don't know how to insert the symbols.


The Attempt at a Solution


I am stuck at these equations because I don't know how to find the area of the wings or the distance between the wings and the ground (no dimensions were given for either). Furthermore I don't know if I even need to use these values at all since I may well be using the wrong equations.
 
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The area of the wings depends on the plane. Make a reasonable assumption or visit the web and look up plane specs. Your equations look correct, but you will also need the equation that gives the capacitance of a parallel plate capacitor.
 
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Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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