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An airplane is flying through a thundercloud at a height of 2000 m (This is a very dangerous thing to do because of updrafts, turbulence, and the possibility of electric discharge.) If there is a charge concentration of 40 C at height 3000 m with the cloud and -40 C at height 1000 m, what is the electric field at the aircraft

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boffeemadrid

Answer:

[tex]400000\ \text{N/C}[/tex]

Explanation:

[tex]q_1[/tex] = Charge at 3000 m = 40 C

[tex]q_2[/tex] = Charge at 1000 m = -40 C

[tex]r_1[/tex] = 3000 m

[tex]r_2[/tex] = 1000 m

k = Coulomb constant = [tex]9\times10^9\ \text{Nm}^2/\text{C}^2[/tex]

Electric field due to the charge at 3000 m

[tex]E_1=\dfrac{k|q_1|}{r_1^2}\\\Rightarrow E_1=\dfrac{9\times 10^9\times 40}{3000^2}\\\Rightarrow E_1=40000\ \text{N/C}[/tex]

Electric field due to the charge at 1000 m

[tex]E_2=\dfrac{k|q_2|}{r_2^2}\\\Rightarrow E_2=\dfrac{9\times 10^9\times 40}{1000^2}\\\Rightarrow E_2=360000\ \text{N/C}[/tex]

Electric field at the aircraft is [tex]E_1+E_2=40000+360000=400000\ \text{N/C}[/tex].

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