A beam of electrons is directed into uniform electric and magnetic feilds that are at right angles to one another and to the beam direction. The strength of the magnetic feild is 55 mT; the electric feild strength is adjusted to 600 kV m^-1 when the beam passed through the feilds undeflected.

Calculate the speed of the electrons.

Bvq = Eq

v = E/B

Thank you

To calculate the speed of the electrons, we can utilize the fact that the electric and magnetic fields are perpendicular to each other and to the beam direction. In this scenario, the electric field is responsible for providing the necessary force to balance the magnetic force on the electrons.

We can start by determining the force experienced by the electrons due to the magnetic field by using the formula:

F_magnetic = q * v * B

where F_magnetic is the magnetic force, q is the charge of an electron (1.6 x 10^-19 C), v is the velocity of the electrons, and B is the strength of the magnetic field (55 mT or 55 x 10^-3 T).

Next, we can calculate the force experienced by the electrons due to the electric field using the formula:

F_electric = q * E

where F_electric is the electric force and E is the strength of the electric field (600 kV m^-1 or 600 x 10^3 V m^-1).

Since the beam passes through the fields undeflected, the electric force and magnetic force must be equal and opposite:

F_electric = F_magnetic

Substituting the equations for the forces, we get:

q * E = q * v * B

Simplifying and rearranging the equation, we find:

v = (E / B)

Now, we can substitute the given values and calculate the speed of the electrons:

v = (600 x 10^3 V m^-1) / (55 x 10^-3 T)

v ≈ 10.91 x 10^6 m/s

Therefore, the speed of the electrons is approximately 10.91 x 10^6 m/s.