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Statement of a problem № 672

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A space is filled up with a charge with volume density ρ = ρ0e-αr3, where ρ0 and α are positive constants, r is the distance from the centre of this system. Find the magnitude of the electric field strength vector as a function of r. Investigate the obtained expression for the small and large values of r, i.e. at αr3 << 1 and αr3 >> 1.

Solution:
A space is filled up with a charge with volume density ρ = ρ0e-αr3, where ρ0

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