# Calculate the pitch of eletron cyclotron in b field.

• jhwatts
In summary, the problem involves a uniform 26.0 mT magnetic field in the positive z-direction, an electron entering the field with a speed of 5.50E6 and an angle of 30 deg. above the xy-plane, and a defined pitch as the distance between successive loops of a helix with a radius of 1.04 mm. The solution involves using the equation p = r*tan(30) to solve for the pitch and understanding that the electron is moving with constant speed along the z-direction. The pitch can be calculated by finding the distance traveled by the electron in one period at the z-direction.
jhwatts

## Homework Statement

The uniform 26.0 mT magnetic field in the figure points in the positive z-direction. An electron enters the region of magnetic field with a speed of 5.50E6 and at an angle of
30 deg. above the xy-plane.

The problem defines the pitch to be the distance between the sucessive loops of the helix.

## The Attempt at a Solution

I thought i could slove for the pitch by solving p= r*tan(30), i don't know, i have no experience solving this kind of problem.

Last edited:
I think you will get more response in the physics section than in the mathematics section so I am moving this post.

The electron is moving with constant speed allong the z-direction. Do you know why?
Between two sucessive loops the time is one period. Thus the pitch is the distance traveled by the electron in one period at z-direction.

Can you calculated it, now?

## 1. What is the formula for calculating the pitch of an electron in a magnetic field?

The formula for calculating the pitch of an electron in a magnetic field is p = eB/mv, where p is the pitch, e is the charge of the electron, B is the magnetic field strength, m is the mass of the electron, and v is the velocity of the electron.

## 2. How do I determine the direction of the pitch of an electron in a magnetic field?

The direction of the pitch of an electron in a magnetic field is determined by the direction of the magnetic field and the direction of the electron's velocity. The pitch will be in the same direction as the magnetic field if the electron is moving parallel to the field, and in the opposite direction if the electron is moving perpendicular to the field.

## 3. What units should I use for the variables in the pitch calculation formula?

The pitch calculation formula should be used with the following units: p in meters, e in coulombs, B in teslas, and m and v in kilograms and meters per second, respectively.

## 4. Can the pitch of an electron change in a constant magnetic field?

No, the pitch of an electron will remain constant in a constant magnetic field, as long as the electron's velocity and the field strength do not change.

## 5. How does the pitch of an electron affect its trajectory in a magnetic field?

The pitch of an electron determines the radius of its circular motion in a magnetic field. A larger pitch will result in a larger radius, while a smaller pitch will result in a smaller radius. This means that the pitch determines the curvature of the electron's trajectory in a magnetic field.

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