Electric charge can accumulate on an airplane in flight. You may have observed n

Question

Electric charge can accumulate on an airplane in flight. You may have observed needle-shaped metal extensions on the wing tips and tail of an airplane. Their purpose is to allow charge to leak off before much of it accumulates. The electric field around the needle is much larger than the field around the body of the airplane and can become large enough to produce dielectric breakdown of the air, discharging the airplane. To model this process, assume that two charged spherical conductors are connected by a long conducting wire and a charge of 79.0 µC is placed on the combination. One sphere, representing the body of the airplane, has a radius of 6.00 m, and the other, representing the tip of the needle, has a radius of 2.00 cm.

(a) What is the electric potential of each sphere? r = 6.00 m: ]V

r = 2.00 cm: V

(b) What is the electric field at the surface of each sphere?

r = 6.00 m: magnitude____________ V/m? direction_________?

r = 2.00 cm: magnitude ____________ V/m? direction________?

Explanation / Answer

a )

r1 = 6 m

r2 = 2 cm = 0.02 m

q1 / q2 = r1 / r2

q1 / q2 = 6 / 0.02 = 300

q1 = 300 q2

q1 + q2 = 79 X 10-6

300 q2 + q2 = 79 X 10-6  

q2 = 2.62 X 10-7 C

q1 = 300 q2

q1 = 300 X 2.62 X 10-7

q1 = 7.87 X 10-5 C

Potential V1 = K q1 / r1

= 9 X 109 X 7.87 X 10-5 / 6

V1 = 118050 volts

towards sphere

Potential V2 = K q2 / r2

= 9 X 109 X 2.62 X 10-7 / 0.02

V2 = 117900 volts

away sphere

b )

E1 = K q1 / r12

E1 = 9 X 109 X 7.87 X 10-5 / 62

E1 = 19675 N/C

towards sphere

E2 = K q2 / r22

E2 = 9 X 109 X 2.62 X 10-7 / 0.022

E2 = 5895000 N/C

away sphere

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