Static Electricity Legacy Problem #16 Guided Solution

This question pertains to the concept of an electric field, and that concept is that any object which accumulates a charge alters the space which surrounds it, such that any object brought into that space will experience a force as a result of that electric field, or that alteration of the space surrounding the charged object. So here, we have a dust particle brought into the space, the atmosphere surrounding the Earth. We're told that in that atmosphere, the strength of the electric field that's created by the Earth is 150 newtons per coulomb. Now, if you focus on the units, they're 150 N divided by C. That's the amount of force on a coulomb of charge running in the space. Now, we're bringing a dust particle into the space, and it doesn't nearly have a coulomb of charge, so we won't nearly get 150 newtons of force upon that dust particle. You'd have to have one coulomb to get 150 newtons of force. So that little 150 newtons per coulomb is simply an F per Q ratio, where F is the force and Q is the quantity of charge brought into the space surrounding the Earth. So, if we wish to calculate the force upon the dust particle, we need to use the equation that the E, 150 newtons per coulomb, is equal to F per Q, and rearrange it such that F is equal to E times Q, and multiply the 150 newtons per coulomb times the 9.2 times 10 to the negative 16th coulombs, and you would get 1.3 times 10 to the negative 13th, and that would be in units of newtons. We can round that to two significant digits. Now, there's something else going on here, and there's something else that's going on. It's the direction of the electric field, and by definition, we describe, we define the direction of the electric field as the direction that a positively charged particle would be pushed or pulled when put in the space surrounding the Earth. So, if we describe the direction of the electric field around the Earth, the Earth's electric field is pointing towards the center of the Earth, and that means any positive charge that was brought into that space would be pulled towards the center of the Earth. That's just simply our convention for the direction of an electric field. So, if this dust particle charged positively, it would be pulled towards the center of the Earth. That tells us that the Earth's got an overall negative charge, but the dust particle isn't charged positively. We're told it's charged with a negative charge, and so unlike the positively charged particle, which is pulled towards the Earth, this dust particle would be pushed away from the Earth, and thus the direction of the force is away from the Earth.