Force acting on a particle between a tube and a wire (elektrodynamics)

[fara0815]

Hello physics community!

After working on this problem for more than 4 hours and reading about the topic in different books, I decided to ask here for help since I do not seem to have a clue.

"A counting tube for a particle accelerator consists of a thin-walled metal tube and a wire that goes along the tube's center axis. The tube has a radius of 12 mm and the wire of 12 X 10^-6 m. Between the tube and the wire there is a current of 1000 volts.

a) Calculate the factor of which the force acting on a particle increases on its way from the tube's wall to the wire.
Answer: 400 times

I have problems to make a connection between the 1000 volts and the electric field with which I could calculate a force (according to Gauss).

What could I start with?

Any help will be appreciated!

 

[Hootenanny]

What can you say bout the field between the wire and the pipe? How does the field vary with distance?

 

[fara0815]

mh, I guess that in the tube's center there is no field at all since all the field lines eliminate each other in the center. So only the wire's field is acting?
The wire can also being considert a point with the electric field of
$$E=\frac{q}{4\pi e} \frac{1}{r^2}$$

Am I getting closer?

 

[Hootenanny]

I was thinking more that the field is uniform. How does the electric field vary with respect to distance in an uniform field?

Also, just a slight correct; I'm sure you meant a potential of 1000V;

Between the tube and the wire there is a current of 1000 volts

 

[fara0815]

I am really sorry but I am not making any progress. If the field is uniform, it does not change its intensity in respect to distance, right ?

What am I missing?

 

[fara0815]

By dividing the electrical potential by the radius, I get a electric field of 83333 V/m.
Is this part of the way I have to take ?

 

[fara0815]

I still cannot figure it out :(

 

[fara0815]

Nobody has an idea?

 

[fara0815]

I think I have got it!

Since the electric field is uniform, the equation to get the electric field is:
$$E= \frac{U}{r}$$ where r is the distance to the particle.
$$r_{tube}=0,012m$$ and $$r_{wire}=3 x 10^-5m$$
$$E_{tube}=\frac{1000V}{0,012m}= 83333.3 Vm$$ and for the wire
$$E_{wire}=\frac{1000V}{3 x 10^-5m}= 33333333.3 Vm$$
for the ratio you do:
$$\frac{E_{wire}}{E_{tube}}= 400.000$$

I think that is it !

 

[Hootenanny]

I think I have got it!

Since the electric field is uniform, the equation to get the electric field is:
$$E= \frac{U}{r}$$ where r is the distance to the particle.
$$r_{tube}=0,012m$$ and $$r_{wire}=3 x 10^-5m$$
$$E_{tube}=\frac{1000V}{0,012m}= 83333.3 Vm$$ and for the wire
$$E_{wire}=\frac{1000V}{3 x 10^-5m}= 33333333.3 Vm$$
for the ratio you do:
$$\frac{E_{wire}}{E_{tube}}= 400.000$$

I think that is it !

Looks good to me . Just one question however, in your initial problem you stated that the radius of the tube was 12 X 10^-6 m, was this a typo? (I was wondering why tmy numbers didn't make sense )

 

[fara0815]

Looks good to me . Just one question however, in your initial problem you stated that the radius of the tube was 12 X 10^-6 m, was this a typo? (I was wondering why tmy numbers didn't make sense )

Oh, I am sorry. You are right, it is a typo. It is supposed to be 30 x 10^-6m :)