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 7.00

Explanation / Answer

Since both spheres must be at same potential

KQ1/r1=KQ2/r2

=>Q1=Q2(r1/r2)------------1

Given

Q1+Q2=7*10-6

Q2(r1/r2)2+Q2=7*10-6

Q2[(6/2)+1]=7*10-6

Q2=1.75*10-6 C

=>Q1=7*10-6-1.75*10-6=5.25*10-6 C

Electric potential at r=6 cm

V6=(9*109)(5.25*10-6)/0.06 =7.875*105 Volts

Electric potential at r=2 cm

V2=(9*109)(1.75*10-6)/0.02 =7.875*105 Volts

b)

at r=6 cm

E6=V/d=7.875*105/0.06=1.3125*107 V/m

at r=2cm

E2=V/d=7.875*105/0.02=3.9375*107 V/m

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