An ion source is producing ^6 Li ions, which have charge +e and mass 9.99 ×10^-27 kg. The ions

An ion source is producing ^6 Li ions, which have charge +e...

Key Concepts

Energy Conversion in Accelerated Charged Particles

This concept involves the transformation of electrical potential energy into kinetic energy when a charged particle is accelerated by an electric field. Here, the kinetic energy gained by a charged ion moving through a potential difference is calculated using the equation (1/2)mv² = qV, allowing for the determination of the particle’s velocity. This fundamental principle underlies how ion sources and accelerators work by converting voltage into motion.

Lorentz Force

The Lorentz force is the combined force exerted on a charged particle by electric and magnetic fields, described by F = q(E + v × B). In situations where the particle experiences both electric and magnetic fields, this force determines the trajectory of the charged particle. Understanding the balance between the magnetic force (qvB) and the electric force (qE) is crucial when arranging conditions for an ion to travel undeflected.

Velocity Selector

A velocity selector is a device that uses perpendicular electric and magnetic fields to filter charged particles by velocity. The device exploits the condition where the electric force exactly cancels the magnetic force, allowing only particles with a specific speed (v = E/B) to pass through undeflected. This concept is essential for experiments and applications where precise control over particle trajectories is needed.

Transcript

00:01 Ok, folks.

00:01 So in this video, we're gonna be talking about the following problem.

00:05 We have, ah, charge source that it's producing by owns, which has a charge of positive e at past 9.99 times 10 to the negative 27 kilograms.

00:18 And thes little charged particles are being accelerated by a potential difference of 10 killer votes.

00:25 And they're passing the horizontally into a region in which there is a uniform vertical be filled of magnitude one point to tesla's, or to be calculating the strength of the smallest e field to be set up over the same region that will allow the ions they charged particles to pass through on deflected.

00:48 So in order to do this probable, first of all, this problem is relatively speaking, more involved than than some of the other problems i've seen.

00:58 But but still, it's really not that bad.

01:01 So in order to do this problem, we need a first understanding, right? so basically, we have, you know, a bunch of you know, little charged particles ions, and we know the charge.

01:14 We know their mess and, you know, they're coming in with a velocity v and the coming in to this region where there is a uniform be found, the magnitude of which we also know to be one point to tesla's or is that this is all of this is the byfield doesn't have to be pointing upward.

01:35 I'm just it could be pointing downward as well.

01:38 It was.

01:39 The direction of the byfield is not really specified in this problem.

01:43 So we're gonna be assuming that it's pointing upward.

01:46 Um, so these all of these air, the byfield and their uniform, their vertical.

01:55 And, you know, once these little particles surpassed once they have entered this region, what they're gonna do if you do, if you do your right hand rule if you remember your formula f equals q times v crosbie for a charged particle.

02:13 Excuse my handwriting or a charged particle moving in a uniform be felled.

02:18 There is gonna be a force.

02:20 Once this particle enters this region right under this region, there's gonna be a force, and that force is gonna be pointing in a direction according to this formula.

02:34 So this formula tells me that if he if this is x hat and v is excited in the exact direction and this is why hat? so this is ecstasy.

02:44 Why so ex crosswise obviously in a d direction.

02:48 So v crosbie gives you a four specter that points straight out of a screen pointing straight at you.

02:55 Ok, so so this particle wants the understeer is gonna is gonna jump out of the screen, especially we just gonna, you know, get deflected in the seat direction.

03:08 Um, so in order for it not to be deflected, what we're gonna do is we're gonna set up in e felled, which is going to attract the particle, or are, you know, do something to the particle.

03:25 To the effect where, um where it exactly counter balances the effect of that be felled, you know, because the byfield is making the particle and jump out of the screen.

03:35 We want an e felt that makes the particle.

03:38 You know, stay inside of the screen, stay inside the x y plane.

03:43 So that's basically what we're doing.

03:45 We have a b field that's trying to deflect the particle.

03:48 We wanna have an e feld that makes the particle stay in its plane in the x y plane and where we want to calculate the minimum strength of that.

03:59 He felt, in other words, the main the minimum, you know, absolute value of that.

04:05 You failed.

04:08 So we know the evil has to be pointing, uh, in the opposite direction of the of the intended deflection direction of the particle, which is the sea had direction.

04:20 Anyway, um, so the first thing we need to dio is tohave the following equation.

04:28 So force equals q times v.

04:33 Crosbie.

04:35 If there is no e field, um, plus the field because we wanna have a new field.

04:41 Um, and this is you go to em a, um remember, this is a this is a vector equation.

04:53 So what we're gonna do is we're going to say that the g component of the force is equal to z component of this vector, and it's also you go to the z component of this vector, which is a z component, and now what we could d'oh is v across b plus e...

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