Velocity selector: An electron moving with a velocity = 5.0 × 10⁷ m/s enters a region of space where perpendicular electric and a magnetic fields are present. The electric field is = . What magnetic field will allow the electron to go through the region without being deflected?

Question

Quizplus · Accepted Answer

The velocity selector principle states that if an electron with a specific velocity is passed through mutually perpendicular electric and magnetic fields, such that the force on the electron due to the electric field is equal and opposite to the force on it due to the magnetic field, then the electron will experience no net force and will pass through the fields undeflected.

Using the formula for the force on an electron due to electric and magnetic fields,
F_electric = q * E = - m * a
and
F_magnetic = q * v * B = m * a

where q is the charge of an electron, E is the electric field, v is the velocity of the electron, B is the magnetic field, and a is the acceleration of the electron.

Equating the two forces and solving for B, we get:
B = E / v
Substituting the given values, we get:
B = (1.1 × 10^4 N/C) / (5.0 × 10^5 m/s) = 2.2 × 10^-2 T

Therefore, the magnetic field required for the electron to go through the region undeflected is 2.0 × 10^-2 T, which is given by choice C.

Velocity Selector: an Electron Moving with a Velocity =