Two small balls, each of mass 5.0 g, are attached to silk threads 50 cm long, which are in turn tied to the same point on the ceiling, as shown below. when the balls are given the same charge q, the threads hang at 5.0° to the vertical, as shown below. what is the magnitude of q? what are the signs of the two charges?

In triangle ABC

Sin5 = BC/AC

BC = (AC) Sin5

BC = (50) Sin5 = 4.36 cm

r = distance between the two balls = 2 BC = 2 x 4.36 = 8.72 cm = 0.0872 m

q = charge on each ball

m = mass of each ball = 5 g = 0.005 kg

electric force between the two balls is given as

F =

using equilibrium of force in vertical direction

T Cos5 = mg eq-2

Using equilibrium of force in horizontal direction

T Sin5 = F eq-3

dividing eq-3 by eq-2

T Sin5 /(T Cos5) = F/mg

F = mg tan5

using eq-1

= mg tan5

inserting the values

= 0.005 x 9.8

q = 2.03 x 10⁻⁷ C

sign of charge is same on both the balls. either it is negative or positive

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.