Question

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.

Answer 1

Answer:

324795 C

252.637820565 N/C

$2.235844712\times 10^{-9}\ C/m^2$

Explanation:

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

R = Radius of Mars = $3.4\times 10^6\ m$

A = Area = $4\pi R^2$

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

Electric flux is given by

$\phi=\dfrac{q}{\epsilon_0}\\\Rightarrow q=\phi\epsilon_0\\\Rightarrow q=3.67\times 10^{16}\times 8.85\times 10^{-12}\\\Rightarrow q=324795\ C$

The charge is 324795 C

Electric field is given by

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

The electric field is 252.637820565 N/C

Surface charge density is given by

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

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