# Electron in magnetic field, quick fix

In summary, the electron with a speed of 3.7e5 m/s enters a uniform magnetic field of magnitude 0.042 T at an angle of 39 degrees to the magnetic field lines. The electron follows a helical path with a radius of 7.906e-5 m, calculated using the formula r = (mv)/(qBsin(39)). However, the correct answer for the radius is 3.1e-5 m, indicating an error in the calculation. The speed of the electron along the circular projection of the helical path is not the same as the total speed.
An electron with speed of 3.7e5 m/s enters a uniform magnetic field of magnitude 0.042 T at an angle 39 degrees to magnetic field lines. The electron will follow a helical path.

Determine the radius of the helical path.

F = (mv^2)/r
F = vq * Bsin(39)
set F's equal and solve for r

r = (mv)/(qBsin(39))

I solved this using
m = 9.109e-31 kg
q = 1.602e-19 C

the answer i got was 7.906e-5 m
the correct answer is 3.1e-5 m

can someone show me what I am doing wrong?

The electron moves along a helical path. The projection of this path in the plane which is normal to B is a circle. The speed along this circle is not the same as the total speed of the electron.

ehild

## 1. How does a magnetic field affect an electron?

When a magnetic field is applied to an electron, the electron will experience a force perpendicular to both the direction of the magnetic field and the direction of its own motion. This force will cause the electron to move in a circular path, known as circular motion.

## 2. What is the formula for calculating the force on an electron in a magnetic field?

The formula for calculating the force on an electron in a magnetic field is F = qvB, where F is the force, q is the charge of the electron, v is the velocity of the electron, and B is the strength of the magnetic field.

## 3. How does the strength of the magnetic field affect the motion of an electron?

The strength of the magnetic field will determine the magnitude of the force on the electron, as well as the radius of its circular path. A stronger magnetic field will result in a larger force and a smaller radius of circular motion.

## 4. Can the direction of the magnetic field affect the motion of an electron?

Yes, the direction of the magnetic field can affect the motion of an electron. If the direction of the magnetic field is reversed, the direction of the force acting on the electron will also be reversed, causing the electron to move in the opposite direction.

## 5. How does the mass of the electron affect its motion in a magnetic field?

The mass of the electron does not affect its motion in a magnetic field. The force acting on the electron is directly proportional to its charge and velocity, and is independent of its mass.

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