The magnetic field within a long, straight solenoid with a circular cross section and radius r is increasing at a rate of dbdt. part a what is the rate of change of flux through a circle with radius r1 inside the solenoid, normal to the axis of the solenoid, and with center on the solenoid axis? express your answer in terms of the variables r, b, r1, and appropriate constants.

Explanation:

To calculate the rate of change of the flux we have to take into account that the magnetic flux is given by

in this case the direction of B is perpendicular to the direction of A. Hence

and A is the area of a circle:

in this case we are interested in the flux of a area of a lower radius r1. Hence

Finally, the change in the magnetic flux will be

hope this helps!!

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.

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