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

In summary, the conversation discusses the movement of hydrogen ions in the presence of electric and magnetic fields. The first question asks for the value of the potential difference needed for the ions to pass through the fields without being deviated, and the answer is 0.1V. The second question asks for the kinetic energy of the ions as they leave the fields, and the answer is 8.4 * 10-24 J. Different attempts at solving the problem are also mentioned, including using the formula F = B e v to calculate the force needed to overcome the magnetic field. The conversation also touches on the purpose of the parallel plates and the importance of considering only electric and magnetic forces at this stage.
  • #1
moenste
711
12

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.

5718ee396b15.jpg


(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.
 
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  • #2
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.
 
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  • #3
gneill said:
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?

gneill said:
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!
 
  • #4
moenste said:
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!
:smile:
 
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  • #5
gneill said:
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?
 
  • #6
moenste said:
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?
 
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  • #7
gneill said:
1 what?
Don't know. It only says something like this. Couldn't find a clear number. Some +1 or 1+ everywhere.

gneill said:
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.
moenste said:
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.
 
  • #8
moenste said:
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?
 
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  • #9
moenste said:
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?
 
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  • #10
cnh1995 said:
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.
 
  • #11
moenste said:
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.
 
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  • #12
moenste said:
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?
 
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  • #13
moenste said:
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?
 
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  • #14
gneill said:
What is the charge on an electron?
It's the elementary charge 1.6 * 10-19 C.

gneill said:
What is the charge on a proton?
It says on Wikipedia also 1.6 * 10-19 C...
 
  • #15
moenste said:
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?
 
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  • #16
moenste said:
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.
 
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  • #17
gneill said:
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?

cnh1995 said:
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.
 
  • #18
moenste said:
An "electric field" as mentioned in the problem?
Yes.
moenste said:
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?
 
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  • #19
cnh1995 said:
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 FInitial, then they are experiencing a FE. Field force, so if we want them to continue in the same direction we need FInitial + F = FE. Field.
 
  • #20
moenste said:
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?
 
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  • #21
moenste said:
Hydrogen ions? The plates only create an electric field that makes the ions deviate.

Well, they are moving with FInitial, then they are experiencing a FE. Field force, so if we want them to continue in the same direction we need FInitial + F = FE. Field.
You seem to be multiplying the number forces involved without justification. Now you have FInitial, F, and FE. 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.
 
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  • #22
cnh1995 said:
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?
 
  • #23
moenste said:
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.
 
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  • #24
cnh1995 said:
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?
 
  • #25
moenste said:
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.
 
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  • #26
cnh1995 said:
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?
 
  • #27
moenste said:
F = B e v?
And??
 
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  • #28
cnh1995 said:
And??
B e v = m v2 / r? But mass is not in the picture as you said.
 
  • #29
moenste said:
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?
 
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  • #30
moenste said:
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 :oldconfused: 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?
 
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  • #31
moenste said:

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.

5718ee396b15.jpg


(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
 
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  • #32
cnh1995 said:
No. Read #19 again. Basically, why does the question ask for voltage? Which force does that suggest?
Potential difference? EMF?

gneill said:
I'm not sure why you seem to being denying the existence of the electric field between the plates :oldconfused: 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 said:
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.
 
  • #33
moenste said:
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.
 
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  • #34
moenste said:
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.
 
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  • #35
cnh1995 said:
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.
 
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