Question

Magnetic Force on a Moving Charge

A velocity selector is a simple configuration of electric and magnetic fields that allows only those ions of a particular velocity in a narrow beam of ions to pass through it. A constant electric field E is oriented perpendicularly to a constant magnetic field B. The beam passes through the fields in the third direction, i.e., perpendicular to both E and B. A screen with a small hole blocks all the ions that are deflected away from the straight line through the fields, and allows only those that travelled in a straight line to pass through.

(a) Explain, with a sketch, why this configuration selects for one velocity.

(b) Suggest realistic values for E and B that would select for the velocity 10^5 m/s.

Answer 1

a] The net force on the ions will be:

where Electric field is perpendicular to both velocity of the ions and magnetic field

this force can then be made zero since the resultant force due to magnetic field and due to electric field will lie in this same plane.

then,

for input electric and magnetic field, therefore, there exists only one value of velocity which will give a net force zero thus acting like a velocity selector.

b]

=>

so, E = -vB

v = 10⁵ m/s and let magnitude of magnetic field strength be 1 Tesla

then Electric field strength will be: |E| = 1 x 10⁵ V/m.