Lightning can be studied with a Van de Graaff generator, which consists of a spherical dome on which charge is continuously deposited by a moving belt. Charge can be added until the electric field at the surface of the dome becomes equal to the dielectric strength of air. Any more charge leaks off in sparks as shown in the figure below. Assume the dome has a diameter of 34.5 cm and is surrounded by dry air with a "breakdown" electric field of 4.20*10 6 V/m.
(a) What is the maximum potential of the dome? =..kV
(b) What is the maximum charge on the dome?..μC

a) Maximum potential of the dome = 724.5kV

b) Maximum charge on the dome = 13.9 micro Coulomb

Explanation:

Diameter of the dome = 34.5 cm =34.5/100 = 0.345 m

Radius of the dome = Diameter/2 = 0.345/2 = 0.1725 m

Electric field strength, E = 4.20 * 10⁶V/m

a) Maximum potential of the dome, V = E*r

V =  4.20 * 10⁶ * 0.1725

V = 724500 Volts = 724.5kV

b) Maximum charge on the dome

V = kQ/r

Q = Vr/k

Q = (724500 * 0.1725)/(9*10⁹)

Q = 1.39 * 10⁻⁵C

Q = 13.9 micro Coulomb

Explanation:

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scientific laws are the result of testing theories and proving them to be facts.

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.