If an electron moves perpendicular to the same field with this speed,what is the radius of its circular orbit?
What speed? What kind of field?
To determine the radius of the circular orbit of an electron moving perpendicular to a magnetic field, you can use the equation for the centripetal force.
The centripetal force of a charged particle moving in a magnetic field is given by the equation: F = qvB
Where:
F is the force acting on the charged particle,
q is the charge of the particle (in this case, the charge of an electron, which is -e),
v is the velocity of the particle,
B is the strength of the magnetic field.
The centripetal force required to keep the electron in a circular orbit is provided by the magnetic field. This force is equal to the force required to overcome the kinetic energy of the electron.
The equation for the force required to overcome the kinetic energy is: F = (mv^2) / r
Where:
m is the mass of the electron,
v is the velocity of the electron, and
r is the radius of the circular orbit.
Since these two forces are equal, we can set the equations equal to each other:
qvB = (mv^2) / r
We can simplify this equation by canceling out the mass and the velocity:
qB = v / r
Finally, solving for the radius (r):
r = v / (qB)
Therefore, to find the radius of the circular orbit, you need to know the speed of the electron (v), the charge of the electron (q), and the strength of the magnetic field (B).