Charged particle in B field

Original post by BobbJo

You need a bit of geometry to do the problem. The total deflection of 20° mean how much it is deviated from the original path of motion.

Relate the radius R of the arc of circular motion due to the magnetic force with the radius of the cylinder (r = 5 cm) with the total deflection of 20°.

Then use what you have set up to solve for v:
Bqv = mv^2/R

Reply 2

Original post by Eimmanuel

https://imgur.com/a/2kzqJP8
The situation looks like this ?
How do I calculate what the radius of the motion is?
I don't know how to relate the radii of the circle to the cylinder and the total deflection :/

Reply 3

Original post by BobbJo

https://imgur.com/a/2kzqJP8
The situation looks like this ?

Yes but the region of magnetic field is circular NOT square or rectangle.

Original post by BobbJo

....
How do I calculate what the radius of the motion is?
I don't know how to relate the radii of the circle to the cylinder and the total deflection :/

You need to make use of geometry.

Draw a line from the point of entry to the point of exit to form a chord in a circle (this circle is the region of the magnetic field).
Draw a radius from the point of entry to the center of the circle and then draw a radius from the center of the circle to the point of exit.
In this way, an isosceles triangle is formed. The angles in this triangle is related to the angle of the total deflection.

How does the radii of the arc of circular motion extend from the point of entry and exit respectively outside the magnetic field region to the center of the circular motion?

Reply 4

Original post by Eimmanuel

Yes but the region of magnetic field is circular NOT square or rectangle.

Draw a line from the point of entry to the point of exit to form a chord in a circle (this circle is the region of the magnetic field).
Draw a radius from the point of entry to the center of the circle and then draw a radius from the center of the circle to the point of exit.
In this way, an isosceles triangle is formed. The angles in this triangle is related to the angle of the total deflection.

How does the radii of the arc of circular motion extend from the point of entry and exit respectively outside the magnetic field region to the center of the circular motion?

https://imgur.com/a/HQqYaIV

I omitted the path of the electrons in the field but A and B are points where the electrons enter and leave

I have made an attempt but don't know if this is right? The lines from the point of exit and point of entry intersect and there is an angle 20 degrees between them?

Not sure what the next step is

Reply 5

Original post by BobbJo

https://imgur.com/a/HQqYaIV
I omitted the path of the electrons in the field but A and B are points where the electrons enter and leave
I have made an attempt but don't know if this is right? ….

You have drawn some of the correct stuff but you interpret the info from the question wrong based on your drawing.

Original post by BobbJo

…
The lines from the point of exit and point of entry intersect and there is an angle 20 degrees between them? ….

Not sure the angle 20 degrees is measured from where.

Original post by BobbJo

…..Not sure what the next step is

I have attached a pic that depicts what I have been describing in the previous post.

The red curve line is the path of travel of electron in the magnetic field. The orange line is the radius of the circular motion.
E₁ and E₂ are the point of entry and exit, respectively.
O is the centre of the magnetic field.

One of the key points is knowing how the radius of the circular motion make with the path of the circular motion.
Once this known, relate the radius R of the arc of circular motion due to the magnetic force with the radius of the cylinder (r = 5 cm) with the total deflection of 20°.

Reply 6

Original post by Eimmanuel

One of the key points is knowing how the radius of the circular motion make with the path of the circular motion.
Once this known, relate the radius R of the arc of circular motion due to the magnetic force with the radius of the cylinder (r = 5 cm) with the total deflection of 20°.

Thank you so much, I understand this a lot better now. I worked out v but I got it wrong.

Spoiler

Edit: I just worked it out again! I got the answer. Please disregard the above.

Thanks a million for your invaluable help and insight! The value of e/m_e was given in the question as 1.8 x 10^11, which caused the difference. I truly appreciate your time! Thanks a lot!!

P.S The reason we can deduce the line extended from the exit point backwards intersects at the centre of the circle is because it enters along a radius. Is this right?

(edited 5 years ago)

Reply 7

Original post by BobbJo

Thank you so much, I understand this a lot better now. I worked out v but I got it wrong.

Spoiler

Original post by BobbJo

...P.S The reason we can deduce the line extended from the exit point backwards intersects at the centre of the circle is because it enters along a radius. Is this right?

Partially.

Reply 8

Original post by Eimmanuel

Partially.

What is the full reason? Is it because the path is circular? Then the tangent at the point of exit and the tangent at the point of entry will intersect at a point which is the midpoint of their x-coordinates. Then, since the tangent at the point of entry is horizontal, they must intersect at the same horizontal level as the tangent point of entry, that is along the radius. Then the point of intersection is the centre. Is this correct?

Edit: I'm not sure how I justify that the tangent at the point of exit and the tangent at the point of entry will intersect at a point which is the midpoint of their x-coordinates.

I think this is not a (fully) correct explanation

(edited 5 years ago)

Reply 9

Original post by BobbJo

You seem to get all points but you are not stitching them in a logical way.

First, we are told that "The electron beam enters the field along a radius of the cylinder", this is important and help to simplify the problem.
Next, the magnetic force is providing for the centripetal force that caused the electron travel in an arc of circle. So the electron would also exit along the radius of the cylinder.

(edited 5 years ago)

Reply 10