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 72.0 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:

r = 2.00 m:

r = 6.00 m:

Explanation / Answer

As the spehers are conducting, all the charge will accumulate on the surface. As they are connected by conducting wire, potential at both spheres will be same. They will share the total charge in inverse ratio of their radii. Hence charge on 6cm sphere will be 54uC and on 2cm sphere charge will b 18uC. Potential on surface will be KQ/R. Hence V= 8.08×10^6 V.

Electric field will be KQ/r2. On 6cm sphere E= 1.347×10^8 V/M.

On 2 cm sphere E= 4.04×10^8 V/M.

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