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Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of 3.67×1016 N⋅m2/C⋅ into the planet's surface.Calculate: (a) the total electric charge on the planet; (b) the electric field at the planet’s surface (refer to the astronomical data inside the back cover); (c) the charge density on Mars, assuming all the charge is uniformly distributed over the planet’s surface.

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Answer:

324795 C

252.637820565 N/C

[tex]2.235844712\times 10^{-9}\ C/m^2[/tex]

Explanation:

[tex]\epsilon_0[/tex] = Permittivity of free space = [tex]8.85\times 10^{-12}\ F/m[/tex]

R = Radius of Mars = [tex]3.4\times 10^6\ m[/tex]

A = Area = [tex]4\pi R^2[/tex]

[tex]\phi[/tex] = Electric flux = [tex]3.67\times 10^{16}\ Nm^2/C[/tex]

Electric flux is given by

[tex]\phi=\dfrac{q}{\epsilon_0}\\\Rightarrow q=\phi\epsilon_0\\\Rightarrow q=3.67\times 10^{16}\times 8.85\times 10^{-12}\\\Rightarrow q=324795\ C[/tex]

The charge is 324795 C

Electric field is given by

[tex]E=\dfrac{\phi}{A}\\\Rightarrow E=\dfrac{3.67\times 10^{16}}{4\pi (3.4\times 10^6)^2}\\\Rightarrow E=252.637820565\ N/C[/tex]

The electric field is 252.637820565 N/C

Surface charge density is given by

[tex]\sigma=\dfrac{q}{4\pi R^2}\\\Rightarrow \sigma=\dfrac{324795}{4\pi (3.4\times 10^6)^2}\\\Rightarrow \sigma=2.235844712\times 10^{-9}\ C/m^2[/tex]

The surface charge density is [tex]2.235844712\times 10^{-9}\ C/m^2[/tex]

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