Calculate Magnetic Field & Velocity of Free Electron @100 nm

[amph1bius]

How would i start to derive the magnetic field intensity and initial velocity for a free electron to circle around a radius of 100 nm?

 

[dextercioby]

The radius is not enough...You need to know the either the period,the frequency/angular velocity or the tangential velocity...

U can then find B.

Daniel.

 

[R0man]

To calculate the magnetic field intensity and initial velocity of a free electron circling around a radius of 100 nm, we can use the equation for the centripetal force:

F = mv^2/r

Where:
F = Centripetal force (N)
m = Mass of the electron (kg)
v = Velocity of the electron (m/s)
r = Radius of the circular path (m)

We can rearrange this equation to solve for the velocity of the electron:

v = √(Fr/m)

Now, we need to find the centripetal force acting on the electron. This is provided by the magnetic force, which is given by the equation:

Fm = qvB

Where:
Fm = Magnetic force (N)
q = Charge of the electron (C)
v = Velocity of the electron (m/s)
B = Magnetic field intensity (T)

We can substitute the expression for Fm into the equation for the centripetal force:

F = (qvB)v

Simplifying:

F = qv^2B

Now, we can substitute this expression for F into the equation we derived for the velocity of the electron:

v = √((qv^2B)r/m)

Simplifying:

v = √(qBr^2/m)

To find the initial velocity of the electron, we need to know the charge and mass of the electron, as well as the magnetic field intensity. We can find the charge and mass of the electron from a standard reference table, and the magnetic field intensity can be obtained through experimental data or a calculation based on the current and distance from a magnetic source.

Once we have these values, we can plug them into the equation to find the initial velocity of the electron. This will give us the velocity at which the electron needs to move in order to maintain a circular path with a radius of 100 nm.

In summary, to derive the magnetic field intensity and initial velocity for a free electron to circle around a radius of 100 nm, we need to use the equations for centripetal force and magnetic force, and rearrange them to solve for the velocity of the electron. We also need to know the charge and mass of the electron, as well as the magnetic field intensity.