In a mass spectrometer, a specific velocity can be selected from a distribution by injecting charged particles between a set of plates with a constant electric field between them and a magnetic field across them (perpendicular to the direction of particle travel). if the fields are tuned exactly right, only particles of a specific velocity will pass through this region undeflected. consider such a velocity selector in a mass spectrometer with a 0.115 t magnetic field. a. what electric field strength, in volts per mater, is needed to select a speed of 3.7 x 10^6 m/s? b. what is the voltage, in kilovolts, between the plates if they are separeted by 0.75 cm?

(a)

In a velocity selector, the speed of the beam is related to the magnitude of the electric field and of the magnetic field by the formula:

where

E is the magnitude of the electric field

B is the magnitude of the magnetic field

In this problem, we have

(magnetic field)

(speed of the particles)

Solving the equation for E, we find the electric field:

(b) 3.2 kV

The relationship between electric field and potential difference between the two plates is:

where, in this problem:

is the magnitude of the electric field

is the separation between the plates

Substituting into the equation, we find the potential difference:

c.the charges if the proton and electron and gravity