What is the magnetic field produced by an electron beam in a cathodic ray tube?

In summary: You have to find a way to calculate the magnetic field produced by a current i that is going around a circle. Can you think of a formula for that?In summary, the conversation discusses how to find the magnetic field produced by a circular electron beam on a point located at a certain distance from the beam axis. The formula for the magnetic field of a circular arc is suggested but deemed incorrect due to the lack of angle. Ampere's law is then brought up as a possible solution, with the knowledge that the magnetic field lines take the shape of a circle around a current flowing in a straight line. The problem is simplified by calculating the current and using a line integral, making the calculation relatively simple. The kinetic energy is deemed irrelevant in this
  • #1
fishingspree2
139
0

Homework Statement


In a cathodic ray tube, the canon launches a circular electron beam on the screen. The beam has a 0.22 mm diameter, the electrons have a kinetic energy of 25 keV and 5.6*10^14 electrons reach the screen each second. Find the magnetic field produced by the beam on a point located at a 1.5mm distance of the beam axis.

The answer is 12 nT


Homework Equations


I know that the magnetic field of a circular arc is
B = (u*i*angle)/(4*Pi*distance) but in this case I don't have an angle so I am pretty sure this is not the correct formula

Also we could integrate using the biot savart rule but we don't have the limits of integration.


The Attempt at a Solution


I have found the current by using the fact that 5.6*10^14 electrons reach the screen each second. By converting electrons to coulombs, I get 8.97 * 10^-5 Amperes. Then I am stuck, I have no idea how to continue

thank you
 
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  • #2
You should review Ampere's law. Particularly the integral form. By the way, do you remember the shape of the magnetic field line in the vicinity of a current flowing in a straight line?
 
  • #3
A circle I believe?
 
  • #4
I still can't do it =( I don't understand what to do with the kinetic energy... I can find the electrons velocity but it would only be useful in the formula F = q v x B and I don't think that would apply here
 
  • #5
fishingspree2 said:
A circle I believe?

Yes, the magnetic field lines take the shape of a circle going around a current i that is traveling in a straight line.

Now do you know Ampere's law? You have already found the magnitude of the current. Ampere's law involves a line integral taken over a suitable path. This actually is a very simple problem once you check your textbook (or Wikipedia). You will have to simplify a dot product, but that should be no problem.
 
  • #6
fishingspree2 said:
I still can't do it =( I don't understand what to do with the kinetic energy... I can find the electrons velocity but it would only be useful in the formula F = q v x B and I don't think that would apply here

The kinetic energy is a red herring and F = qv X B is useless in this context.
 

1. What is a magnetic field problem?

A magnetic field problem is a scientific or engineering problem that involves understanding, predicting, or controlling the behavior of magnetic fields. This could include phenomena such as the movement of charged particles in a magnetic field or the interaction between magnetic fields and materials.

2. How do magnetic fields affect everyday life?

Magnetic fields play a crucial role in many everyday technologies, such as electric motors and generators, MRI machines, and magnetic storage devices. They also play a role in natural phenomena like the Earth's magnetic field, which helps protect us from harmful solar radiation.

3. What factors affect the strength and direction of a magnetic field?

The strength and direction of a magnetic field can be affected by a number of factors, including the strength and orientation of the source of the magnetic field, the type of material the magnetic field is passing through, and the presence of other magnetic fields nearby.

4. How do scientists study magnetic fields?

Scientists use a variety of tools and techniques to study magnetic fields, such as magnetometers, which measure the strength and direction of magnetic fields, and numerical simulations, which use mathematical models to predict the behavior of magnetic fields.

5. What are some potential applications of understanding and controlling magnetic fields?

Understanding and controlling magnetic fields has many potential applications, including in energy production and storage, transportation, medical imaging, and materials science. It also has potential applications in space exploration, such as shielding spacecraft from radiation and navigating using the Earth's magnetic field.

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