Spectrometer

Question

 In the velocity selector part of a mass spectrometer, a field of 0.65 T is used for magnetic deflection of a beam of protons travelling at a speed of 1.0 x 106 m/s. What electric field is needed to balance the force due to the magnetic field? If the distance between the plates of the electrical deflection apparatus is 0.50 cm, what voltage must be applied to the plates?

Answer 1

The magnetic and electric forces must be in equilibrium.  Assuming the beam enters the spectrometer in a direction perpendicular to the magnetic field,

 

qvB = qE

 

E = vB

 

Plug in v in m/s and B in Teslas and get E in N/C.

 

For the voltage, recall that for closely spaced parallel plates,

 

E = voltage / (plate separation distance)

 

voltage = E x (plate separation distance) 

 

Plug in E in N/C and separation distance in meters and get voltage in volts.