The figure below shows a small, charged sphere, with a...

The figure below shows a small, charged sphere, with a charge of q = +44.0 nC, that moves a distance of d = 0.197 m from point A to point B in the presence of a uniform electric field E of magnitude 270 N/C, pointing right. (a) What is the magnitude (in N) and direction of the electric force on the sphere? magnitude N direction (b) What is the work (in J) done on the sphere by the electric force as it moves from A to B? J (c) What is the change of the electric potential energy (in J) as the sphere moves from A to B? (The system consists of the sphere and all its surroundings.) PEB - PEA = J (d) What is the potential difference (in V) between A and B? VB - VA = V

Transcript

00:01 Well, in this question, we're given this setup where we have a positive charge in the electric field.

00:04 We're told the charge and electric field and the distance that it travels in that field.

00:09 And we're asked various things, the first of which is, what is the direction and magnitude of the electric force on our charge here? well, we know definitionally our electric force is equal to our charge times our electric field.

00:21 And we have both of those values.

00:24 We have a negative 9 because it's nano coulombs there.

00:29 And then our electric field has a magnitude of 270 newtons per coulomb.

00:33 And if i'm going to say to the right is the positive x direction, this will be acting to the right because i have a positive charge in an electric field.

00:42 And so conventionally, that is going to be the positive direction for force.

00:47 So if i go ahead and plug that in my calculator, i get an electric force of 11 .9 newtons.

00:55 And that's going to be in the i hat direction.

00:57 Part b then asks, what is the work done on the sphere by the electric force? so our work, we know, is equal to our force dotted with our distance vector.

01:11 Well, in this case, our distance vector is going to the right.

01:14 And our electric field and electric force are also going to the right.

01:18 So this is going to just become our electric force times the distance we travel.

01:22 And then the cosine of the angle between them, well, the cosine of the angle between them is going to just be 1 because the angle between them is 0.

01:29 So we really just have our work is equal to our force.

01:34 I also realize this is not 11 .9 newtons.

01:36 This is 11 .9 micronewtons.

01:38 Good on you if you caught that.

01:40 So 11 .9 times 10 to the negative 6 newtons times the distance i travel...

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