Answer: -33.3 * 10^9 C/m^2( nC/m^2)
Explanation: In order to solve this problem we have to use the gaussian law, the we have:
Eoutside =0 so teh Q inside==
the Q inside= 4.6 nC/m*L + σ *2*π*b*L where L is the large of the Gaussian surface and b the radius of the shell.
Then we simplify and get
σ= -4.6/(2*π*b)= -33.3 nC/m^2
Because the polar regions receive low-angle insolation.
Insolation is the amount of solar radiation received by a given area. The Sun is always low on the horizon. The low Sun angle makes the beam of solar radiation to travel a longer distance from upper troposphere to reach earth's surface as compared to when it is directly overhead. In this case, the radiations are scattered and reflected more by the atmosphere and spread over a larger area. Thus, the intensity of solar radiation is very less at polar regions than near the equatorial region. This is the reason of very cold climates at polar regions.
To develop this problem we will start from the definition of entropy as a function of total heat, temperature. This definition is mathematically described as

Here,
Q = Total Heat
T = Temperature
The total change of entropy from a cold object to a hot object is given by the relationship,

From this relationship we can realize that the change in entropy by the second law of thermodynamics will be positive. Therefore the temperature in the hot body will be higher than that of the cold body, this implies that this term will be smaller than the first, and in other words it would imply that the magnitude of the entropy 'of the hot body' will always be less than the entropy 'cold body'
Change in entropy
is smaller than 
Therefore the correct answer is C. Will always have a smaller magnitude than the change in entropy of the cold object
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