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

[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.