# Deflection of beam due to magnetic field

1. Mar 10, 2008

### ttiger2k7

[SOLVED] Deflection of beam due to magnetic field

1. The problem statement, all variables and given/known data

In the electron gun of a TV picture tube the electrons (charge - e, mass m) are accelerated by a voltage V. After leaving the electron gun, the electron beam travels a distance D to the screen; in this region there is a transverse magnetic field of magnitude B and no electric field.

Find the approximate deflection of the beam due to this magnetic field. (Hint: Place the origin at the center of the electron beam’s arc and compare an undeflected beam’s path to the deflected beam’s path.)
Express your answer in terms of the variables B, D, e, m, and V.

2. Relevant equations

E/B = ((2eV)/m)

e/m = 1.758E-11 C/kg

3. The attempt at a solution

I would show my work, but I really have no idea how to. I tried just typing in the equation for E/B, but it didn't work. Is there a specific formula for deflection?

2. Mar 10, 2008

### Hootenanny

Staff Emeritus
There is a specific formula, but it's not an equation that one usually remembers. In any case, I would imagine you are expected to derive such a formula in your working. I'll help you along the way if you like.

A good place to start would be the Lorentz force. What is the magnitude of the force? In what direction does the force act? If a force acts in this direction, what sort of motion results?

3. Mar 10, 2008

### ttiger2k7

Let's see, the magnitude of the Lorentz force is qvB. It acts perpendicular to the force and velocity..am I supposed to know which direction specifically from the information given?

4. Mar 11, 2008

### Hootenanny

Staff Emeritus
Correct. So, do you know of a certain 'type' of motion where the force always acts perpendicular to the velocity?

5. Mar 11, 2008

### ttiger2k7

Is the motion of the lorentz force circular?

6. Mar 11, 2008

### Hootenanny

Staff Emeritus
Indeed, so if the motion is circular can you write down an equation for the radius of the circular path the electron follows whilst in the magnetic field?

7. Mar 11, 2008

### ttiger2k7

Hmm, I believe it's

R = mv/qB

8. Mar 11, 2008

### Hootenanny

Staff Emeritus
Last edited: Mar 11, 2008
9. Mar 11, 2008

### ttiger2k7

Thanks, got it.

10. Sep 8, 2009

### Cahane

Re: [SOLVED] Deflection of beam due to magnetic field

Hi.. I'm new on this forum.. I'm reading this tread and try to learn it. Can you give any other reference link that have a diagram on it. Maybe it was removed from the link you state here because I can't see any diagram.

Thanks