V required so ions passing through the region don't devitate

[moenste]

Homework Statement

Hydrogen ions moving at various speeds are directed at a region of combined electric and magnetic fields as shown in the diagram below. The electric field is between two parallel plates 10 mm apart with a potential difference V across them, while the magnetic field of flux density 0.1 T is at right angles to the electric field.

(a) Calculate the value of V required so that ions of speed 100 m s^-1 pass through the region of the two fields without being deviated.

(b) What is the kinetic energy per ion as they leave the combined fields?

(1 u = 1.67 * 10^-27 kg.)

Answers: (a) 0.1 V, (b) 8.4 * 10^-24 J.

2. The attempt at a solution
(a) Can't get it right. I use 0.5 m v² = e V, where we don't know the mass m. I then tried to use F = B e v = 0.1 * 1.6 * 10^-19 * 100 = 1.6 * 10^-18 N and then F = m g so m = F / g = 1.6 * 10^-18 / 10 = 1.6 * 10^-19 kg -- not correct.

I also used B e v = m v² / r so m = B e r / v = 0.1 * 1.6 * 10^-19 * 0.01 / 100 = 1.6 * 10^-24 kg. Also not correct.

I even thought that since we have hydrogen then its relative atomic mass is 1.008 and so 1.008 * 1.67 * 10^-27 = 1.68 * 10^-27 kg, also not correct.

If we plug in 0.1 V (which we need to find) into the first formula we'll get m = 3.2 * 10^-24 kg. But I've got no idea how to find it.

 

[gneill]

You're plugging in numbers way too soon. Use symbols to start with.

What condition must hold if the ions are not going to be deflected? Can you write an expression for that?

Also, you may want to check that the given answer for part (b) is not a typo. Something on the order of 10^-4 Joules for a single hydrogen ion would be mighty impressive indeed.

 

[moenste]

What condition must hold if the ions are not going to be deflected? Can you write an expression for that?

Maybe you are talking about "An electron moving with velocity v at right angles to a magnetic field of flux density B experiences a force F, which is given by equation F = B e v."? And since the electron experiences this force, in order to move in the same direction it should have F to move + additional F to overcome the magnetic field force. Am I going in the right direction?

Also, you may want to check that the given answer for part (b) is not a typo. Something on the order of 10-4 Joules for a single hydrogen ion would be mighty impressive indeed.

Ah, sorry, it's -24, not -4!

 

[gneill]

Maybe you are talking about "An electron moving with velocity v at right angles to a magnetic field of flux density B experiences a force F, which is given by equation F = B e v."? And since the electron experiences this force, in order to move in the same direction it should have F to move + additional F to overcome the magnetic field force. Am I going in the right direction?

That's the idea. Only in this case the electron is replaced with a hydrogen ion. What's the charge on a hydrogen ion? And what force is it that's providing the "additional F"? What's an expression for that force?

Ah, sorry, it's -24, not -4!

 

[moenste]

That's the idea. Only in this case the electron is replaced with a hydrogen ion. What's the charge on a hydrogen ion? And what force is it that's providing the "additional F"? What's an expression for that force?

Chage on the ion is 1.

Maybe it's F = 2 B e v?

 

[gneill]

Chage on the ion is 1.

1 what?

Maybe it's F = 2 B e v?

Are there two magnetic fields? What is the purpose of the parallel plates?

 

[moenste]

1 what?

Don't know. It only says something like this. Couldn't find a clear number. Some +1 or 1+ everywhere.

Are there two magnetic fields? What is the purpose of the parallel plates?

Maybe I need to have: m = 2 B e r / v = 2 * 1.6 * 10^-24 = 3.2 * 10^-24 kg. Double it, since we have two plates.

I also used B e v = m v2 / r so m = B e r / v = 0.1 * 1.6 * 10-19 * 0.01 / 100 = 1.6 * 10-24 kg. Also not correct.

 

[cnh1995]

Double it, since we have two plates.

What do you think is the purpose of the plates? What forces are acting on the ion when it gets in between the plates?

 

[gneill]

Don't know. It only says something like this. Couldn't find a clear number. Some +1 or 1+ everywhere.

What is the charge on an electron? What is the charge on a proton?

 

[moenste]

What do you think is the purpose of the plates? What forces are acting on the ion when it gets in between the plates?

I'd say they remind me the Hall effect -- two plates that create a magnetic field that makes the particle deviate from its path. Don't know whether this applies here.

 

[gneill]

Maybe I need to have: m = 2 B e r / v = 2 * 1.6 * 10^-24 = 3.2 * 10^-24 kg. Double it, since we have two plates.

Hint: The mass of the particle is irrelevant until you need to talk about kinetic energy. Only magnetic and electric forces are of interest right now.

 

[gneill]

I'd say they remind me the Hall effect -- two plates that create a magnetic field that makes the particle deviate from its path. Don't know whether this applies here.

Plates do not create a magnetic field. What kind of field do they produce when they are supplied with a potential difference?

 

[cnh1995]

I'd say they remind me the Hall effect -- two plates that create a magnetic field that makes the particle deviate from its path. Don't know whether this applies here.

You are close.
Magnetic field will tend to deviate the ion. But if the ion is not supposed to deviate along its way, what will stop it from deviating?

 

[moenste]

What is the charge on an electron?

It's the elementary charge 1.6 * 10^-19 C.

What is the charge on a proton?

It says on Wikipedia also 1.6 * 10^-19 C...

 

[gneill]

It's the elementary charge 1.6 * 10^-19 C.It says on Wikipedia also 1.6 * 10^-19 C...

Right. What's the difference between the two?

 

[cnh1995]

It's the elementary charge 1.6 * 10^-19 C.It says on Wikipedia also 1.6 * 10^-19 C...

You'll soon notice that this value is also not necessary for calculation of V.

 

[moenste]

Plates do not create a magnetic field. What kind of field do they produce when they are supplied with a potential difference?

An "electric field" as mentioned in the problem?

You are close.
Magnetic field will tend to deviate the ion. But if the ion is not supposed to deviate along its way, what will stop it from deviating?

A larger inner force? Like if we have a car which is going on an inclined road and has friction to be overcomed, we need more force.

 

[cnh1995]

An "electric field" as mentioned in the problem?

Yes.

A larger inner force? Like if we have a car which is going on an inclined road and has friction to be overcomed, we need more force.

And who will provide this "inner force" in this problem? Also, should it be larger than the deviating force?

 

[moenste]

And who will provide this "inner force"? Also, should it be larger than the deviating force?

Hydrogen ions? The plates only create an electric field that makes the ions deviate.

Well, they are moving with F_Initial, then they are experiencing a F_{E. Field} force, so if we want them to continue in the same direction we need F_Initial + F = F_{E. Field}.

 

[cnh1995]

Well, they are moving with FInitial

The ion is not moving with an initial force. It has an initial velocity of 100m/s. To maintain that velocity throughout along its way, the ion must experience zero net force(Newton's 1rst law). How is this achieved when the ion is in between the plates?

 

[gneill]

Hydrogen ions? The plates only create an electric field that makes the ions deviate.

Well, they are moving with F_Initial, then they are experiencing a F_{E. Field} force, so if we want them to continue in the same direction we need F_Initial + F = F_{E. Field}.

You seem to be multiplying the number forces involved without justification. Now you have F_Initial, F, and F_{E. Field} without pinning down what they might be or how they are calculated.

There are only two forces operating: The magnetic field and the electric field. You should be able to write expressions for both as they act on the moving particle.

 

[moenste]

The ion is not moving with an initial force. It has an initial velocity of 100m/s. To maintain that velocity throughout along its way, the ion must experience zero net force(Newton's 1rst law). How is this achieved when the ion is in between the plates?

0.5 m v² = e V?
Left is before the field and right is after entering the field?

 

[cnh1995]

0.5 m v² = e V?
Left is before the field and right is after entering the field?

No. The ion enters the plate region with velocity 100m/s. Which forces are acting on it the moment it enters the region? Forget about the situation before the ion enters the plate region. It is not of any use or significance here.

 

[moenste]

No. The ion enters the plate region with velocity 100m/s. Which forces are acting on it the moment it enters the region? Forget about the situation before the ion enters the plate region. It is not of any use or significance here.

F = m g and F = m a?

 

[cnh1995]

F = m g and F = m a?

Again, mass is not in the picture here because gravity doesn't affect subatomic particles. You yourself have recognized the two forces earlier, but in two separate posts.

 

[moenste]

Again, mass is not in the picture here because gravity doesn't affect subatomic particles. You yourself have recognized the two forces earlier, but in two separate posts.

F = B e v?

 

[cnh1995]

F = B e v?

And??

 

[moenste]

And??

B e v = m v² / r? But mass is not in the picture as you said.

 

[cnh1995]

B e v = m v² / r? But mass is not in the picture as you said.

No. Read #19 again. Basically, why does the question ask for voltage? Which force does that suggest?

 

[gneill]

B e v = m v² / r? But mass is not in the picture as you said.

I'm not sure why you seem to being denying the existence of the electric field between the plates You seem to be going out of your way to avoid mentioning it. Perhaps you haven't been introduced to electric fields between parallel plates?

The purpose of the plates with a potential difference V is to establish an electric field between them. Now. What is the force on a charge in a uniform electric field E?

 

[lychette]

Homework Statement

Hydrogen ions moving at various speeds are directed at a region of combined electric and magnetic fields as shown in the diagram below. The electric field is between two parallel plates 10 mm apart with a potential difference V across them, while the magnetic field of flux density 0.1 T is at right angles to the electric field.

(a) Calculate the value of V required so that ions of speed 100 m s^-1 pass through the region of the two fields without being deviated.

(b) What is the kinetic energy per ion as they leave the combined fields?

(1 u = 1.67 * 10^-27 kg.)

Answers: (a) 0.1 V, (b) 8.4 * 10^-24 J.

2. The attempt at a solution
(a) Can't get it right. I use 0.5 m v² = e V, where we don't know the mass m. I then tried to use F = B e v = 0.1 * 1.6 * 10^-19 * 100 = 1.6 * 10^-18 N and then F = m g so m = F / g = 1.6 * 10^-18 / 10 = 1.6 * 10^-19 kg -- not correct.

I also used B e v = m v² / r so m = B e r / v = 0.1 * 1.6 * 10^-19 * 0.01 / 100 = 1.6 * 10^-24 kg. Also not correct.

I even thought that since we have hydrogen then its relative atomic mass is 1.008 and so 1.008 * 1.67 * 10^-27 = 1.68 * 10^-27 kg, also not correct.

If we plug in 0.1 V (which we need to find) into the first formula we'll get m = 3.2 * 10^-24 kg. But I've got no idea how to find it.

The ions experience a force due to the electric field between the parallel plates...do you know how to calculate this?
They also experience a force due to the magnetic field...do you know how to calculate this

 

[moenste]

No. Read #19 again. Basically, why does the question ask for voltage? Which force does that suggest?

Potential difference? EMF?

I'm not sure why you seem to being denying the existence of the electric field between the plates You seem to be going out of your way to avoid mentioning it. Perhaps you haven't been introduced to electric fields between parallel plates?

The purpose of the plates with a potential difference V is to establish an electric field between them. Now. What is the force on a charge in a uniform electric field E?

The ions experience a force due to the electric field between the parallel plates...do you know how to calculate this?
They also experience a force due to the magnetic field...do you know how to calculate this

F = e V in electric and F = B e v in magnetic fields?

e V = B e v
V = B v = 0.1 * 100 = 10 V, not 0.1 V.

 

[gneill]

F = e V in electric and F = B e v in magnetic fields?

The second one is correct but the first is not. You should familiarize yourself with the difference between potential difference V in Volts (which is a name given to the unit combination Joules/Coulomb) and an electric field E in Volts/m (which is also the same as Newtons per Coulomb). e V (charge in Coulombs times potential difference in Volts) would yield a result in Joules (energy) not a force.

The potential difference between the plates (V) establishes an electric field (E) in the gap between the plates. You should do a bit of research on this so you know how to determine one from the other. Perhaps look up "electric field parallel plates" with a search engine.

 

[cnh1995]

e V = B e v

First term is incorrect. And the charge should be q instead of e since the ion is not an electron.

 

[gneill]

First term is incorrect. And the charge should be q instead of e since the ion is not an electron.

e is commonly used to refer to the unit of elementary charge though, so it actually works in this case. I'd be more picky about this if the ions involved had a different charge than a single elementary charge.

 

[moenste]

First term is incorrect. And the charge should be q instead of e since the ion is not an electron.

e is commonly used to refer to the unit of elementary charge though, so it actually works in this case. I'd be more picky about this if the ions involved had a different charge than a single elementary charge.

Maybe it's e E = B e v?

 

[cnh1995]

Maybe it's e E = B e v?

Right. So how would you proceed then?

 

[gneill]

Maybe it's e E = B e v?

Yes, that is a valid expression of the condition that the magnitude of the electric force balances the magnitude of the magnetic force on the moving charge. The result of course is no net force, so no deviation.

 

[moenste]

Right. So how would you proceed then?

E = B v = 0.1 * 100 = 10 V, not 0.1 V.

 

[cnh1995]

E = B v = 0.1 * 100 = 10 V, not 0.1 V.

That is the expression for electric field, not voltage. How is electric field related to voltage?

 

[gneill]

E = B v = 0.1 * 100 = 10 V, not 0.1 V.

You've found the magnitude of E, but check your units: The units of E are not volts! What's the expression for the electric field established between parallel plates?

 

[moenste]

That is the expression for electric field, not voltage. How is electric field related to voltage?

E = V / d?

 

[gneill]

E = V / d?

Yes!

It's easy to remember because the units of E are volts/m.

 

[moenste]

Yes!

It's easy to remember because the units of E are volts/m.

Why do we need it? We need to find V and we don't know E.

 

[gneill]

Why do we need it? We need to find V and we don't know E.

You found E in post #39.

 

[moenste]

You found E in post #39.

So, E = V / d, V = B v d = 0.1 * 100 * (10 / 10 / 100) = 0.1 V.

How do we find the kinetic energy per ion?
KE = 0.5 m v² = 0.5 * 1.67 * 10^-27 * 100² = 8.35 * 10^-24 J?

 

[gneill]

So, E = V / d, V = B v d = 0.1 * 100 * (10 / 10 / 100) = 0.1 V.

How do we find the kinetic energy per ion?
KE = 0.5 m v² = 0.5 * 1.67 * 10^-27 * 100² = 8.35 * 10^-24 J?

Yes and yes.