An airplane is flying through a thundercloud at a height of 2,500 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 +31 C at height 4,000 m within the cloud and −31 C at height 500 m,what is the magnitude of the electric field E at the aircraft? (k_e = 8.99 × 10⁹ N·m²/C²)

Question

Quizplus · Accepted Answer

First, we need to find the net charge within the region where the aircraft is flying:
Q = Q_above - Q_below
Q = +31 C - (-31 C)
Q = 62 C
Then, we can use Gauss's Law to find the electric field:
∮E⃗ ⋅dA⃗ = Q/ε0
E(4πr^2) = Q/ε0
E = Q/(4πε0r^2)
where r is the distance from the charge concentration to the aircraft. Since the charges are distributed uniformly, we can assume that r is the average distance between the aircraft and the two charge concentrations, which is:
r = (4000 m + 500 m)/2 - 2500 m
r = 1000 m
Plugging in the values, we get:
E = (62 C)/(4π(8.99 × 10^9 N·m^2/C^2)(1000 m)^2)
E ≈ 193,535 N/C, which is answer choice D.

An Airplane Is Flying Through a Thundercloud at a Height