Some planetary scientists have suggested that the planet Mars has...

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 −3.63×1016 N·m2/C at the planet's surface. Calculate:(c) the charge density on Mars, assuming all the charge is uniformly distributed over the planet's surface.

Accepted Answer

Welcome back everybody. We are looking at a spherical dust particle which we are told has an electric flux measured at the surface of negative 1. times 10 to the second. Newton meters squared per cool. Um we're told that the radius of this particle is 10 micro meters or 10 times 10 to the nega six m. And we are tasked with finding what the charge density on the surface of the particle is. What we're going to have to use two formulas. Here we know that the charge density is equal to Q. or the charge enclosed divided by the surface area of the particle. But what is Q enclosed? Well, we can figure out Q enclosed from gasses law that states that the electric flux is equal to Q enclosed divided by the electric Perma titty constant. Now I'm gonna multiply on both sides of this equation by the electric Perma titty constant. And you'll see that on the right here, it cancels out. This leaves us with the fact that Q enclosed is equal to our electric flux times our electric Perma titty constant, which we have both of those values. So let's go ahead and plug that in Our Q. And close is therefore equal to negative 1.4 times 10 to the second, which is our electric flux times our electrical primitively constant of 8.85 times 10 to the negative 12. This gives us that our Q enclosed is equal to negative 1. times 10 to the negative ninth. Great. Now that we have that we are ready and good to go to find our charge density are charged density is going to be our Q enclosed of negative 1.24 times 10 to the ninth, divided by the surface area of our spherical particle. Now this is just going to be four pi times the radius of 10 times 10 to the negative six squared. And when you plug all of this into your calculator, you get that. The charge density on the surface of our spherical particle is negative 60.98 kg per meter squared corresponding to our final answer. Choice of B. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.

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