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A lead nucleus is spherical with a radius of about 7 ✕ 10⁻¹⁵ m. The nucleus contains 82 protons (and typically 126 neutrons). Because of their motions the protons can be considered on average to be uniformly distributed throughout the nucleus. Based on the net flux at the surface of the nucleus, calculate the divergence of the electric field as electric flux per unit volume.

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davidlcastiblanco

Answer:

∈=[tex]3.1584x10^{26} \frac{V}{m}[/tex]

Explanation:

Using the Gauss Law to determine the electric field of the net flux at the surface of the nucleus

∈[tex]=\frac{P}{E_{o}}[/tex]

The P is the charge density and 'Eo' is the constant of permittivity in free space

to find P

[tex]P=\frac{q}{V}[/tex]

[tex]V=\frac{4}{3}*\pi*r^3[/tex]

[tex]V=\frac{4}{3}\pi*(7x10^{-15})^3[/tex]

[tex]V=2.932x10^{-14} m^3[/tex]

[tex]P=\frac{82C}{2.932x10^{-14}m^3}=2.7965x10^{15} \frac{C}{m^3}[/tex]

So replacing

∈[tex]=\frac{2.7965x10^{15}\frac{C}{m^3}}{8.8542x10^{-12}\frac{C^2}{N*m^2}}[/tex]

∈=[tex]3.1584x10^{26} \frac{V}{m}[/tex]

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