Two stationary point charges +3.00 nC and +2.00 nC are separated by a distance of 50.0 cm . An e

step 1 Yeah, All right. So we have question number 23.16 of Chapter 23. Electric potential were given t

Two stationary point charges +3.00 nC and +2.00 nC are...

Key Concepts

Electric Potential Energy

Electric potential energy is the energy stored in a system of charges due to their positions relative to each other. In problems involving point charges, this energy depends on the magnitudes of the charges and the distances between them. It plays a key role in determining how much work will be done when charges move under electrostatic forces.

Conservation of Energy

The conservation of energy principle asserts that the total energy in an isolated system remains constant. In the context of electrostatics, it means that any change in electric potential energy (as a charged particle moves in an electric field) is accompanied by an equal and opposite change in kinetic energy. This concept is essential when relating a particle's potential energy loss or gain to its acceleration or deceleration.

Coulomb's Law

This principle governs the interaction between point charges. It quantifies the force between two charged objects as directly proportional to the product of their charges and inversely proportional to the square of the distance separating them. Understanding Coulomb's Law is fundamental when analyzing how charges influence one another in electrostatic situations.

Dynamics of Charged Particles

This concept involves understanding how particles with electric charge move under the influence of electric forces. The conversion of electric potential energy to kinetic energy (or vice versa) dictates the motion of charges. Analyzing the dynamics typically involves applying both Coulomb's Law and energy conservation principles to determine velocities and trajectories of charged particles.

Transcript

00:01 Yeah, all right.

00:04 So we have question number 23.16 of chapter 23.

00:11 Electric potential were given that there are two charges cuban and q two, so cuban has charged it.

00:20 Calls to three nano column means that three into 10% minus nine column and you do have to nine column.

00:27 So this is 2 to 10% minus nine columns.

00:31 We have electron sitting in the mid point.

00:34 That means this has 0.25 middle distance.

00:38 This has 0.25 million distance.

00:40 The total distance between those two charges this 20.5 m.

00:43 So we have this situation at the beginning.

00:48 These three particles, or the cuban electron judge and q two are sitting on the same line, just a straight line, so we can draw a straight line here.

01:03 So we have a straight line, and this is electron sitting at the center and killed two at the end and cuban and descend so definitely so.

01:27 Electric force will act on this electron, and this electron will move either left or right depends on the cuban magnitude charge in q two magnitude jobs since cuban is higher, that means the force acting on this electron will act higher.

01:48 So let's say this is f one.

01:50 So this is the force acting on electricity to cuban, and this is the force.

01:56 Have to acting on electricity to cuba q.

02:00 Two and we know that forces it cause to one by four by absolute cuban q two over our square.

02:08 This is general formula.

02:09 Our cap are the same.

02:12 We have 0.25 m 0.25 m and cuban is discharge, which is trina column and kyoto is too narrow.

02:21 Column an electron charges 1.6 international minus 19.

02:26 So let me right the electron charge, too.

02:29 So we have electron judge music close to 1.6, the industrial minus 19, since this is negatively charged particles, so they both will attract.

02:44 But cuban is higher charged, so the final force the net force will act towards this way to the election will move from this position to this position somewhere towards cuban.

02:58 So the question is, finally the velocity of the particle riches to some distance here, and the distance between cuban and electron remains.

03:07 We 0.1 m.

03:09 So the remaining let the stands between q two and electron will remain 2.4 m because the distance culturally stands between cuban and cute to his 0.5 m.

03:20 So this is the hour initial situation or before, and this is the final situation or the after situation.

03:28 So particle goes from here to here.

03:31 So at the beginning, the particle has jokinen technology or zero velocity, and it gains someone out to here and reaches to this point.

03:39 And we need to find out the velocity of the particle electron at this position.

03:45 All right.

03:48 Okay.

03:49 Uh, we have used this to formula here than to you.

03:53 Delta used changing potential energy, and this is changing canada energy.

04:10 So at the beginning, there was no kind of technology.

04:12 So that means that the value it calls to kind of energy and we know that kind of energy calls to half every square or half m e massive electron and we square.

04:26 So this way we have to find out the velocity.

04:30 The general formula for you is, of course, one by four by absolute cuban q two over our that minister.

04:35 You see, the prevention is in between cuban and q two and distance between those cuban and q two is our.

04:42 So we have two situations here.

04:43 So we have the force acting on this one between these two and force acting on this one, the force acting between cuba and cuba here.

04:52 But we don't need to care about this situation now because the question doesn't ask anything about cuban and cute to movement.

04:57 So we think that cuban culture doesn't move and there is no change in potentially between before then after situation due to cuba and q two displacement or because there is no displacement between cuba and q two.

05:09 So we don't care about delta.

05:12 You between cuba and cuba, we care about the cuban and electron and q two and electron.

05:19 So let me mark two circles again between these two.

05:23 So so we have two pairs.

05:26 So we have two pairs, these two parents.

05:32 So we have cuban electron and shoot to electoral.

05:39 Yeah, and we will find out the changing potential energy, that changing potential as you will give us the kind of technology and that kind of technology can be used to find out the velocity using this formula.

05:51 All right.

05:59 Yeah, yeah.

06:00 What? yeah, yeah.

06:09 Okay.

06:12 Yeah, just so we have canada.

06:16 Technology is the cause to delta you delta u is your final minus you initial we can take the magnitude doesn't matter because canadian, which is always posted it's always supposed to.

06:31 So if you want to take you i am saying you i minus you have because sometimes if students confused so that i do you have minus u i or u i minus you have in this situation doesn't matter, so we don't we don't care.

06:44 You can take it anyway and just take the positive value of whatever the calculation is.

06:50 So then to you 92 it calls to the changing potential regime, and we have uf minus ui.

07:01 So let's strike you f the final one.

07:05 Okay, coming back to the situation.

07:07 So we have your final, this one.

07:10 So this is the final situation.

07:12 So cuban q to these other players.

07:14 Now the distance between cuban and e is 0.1 m and q two and e s 20.4 m...