Physics-
General
Easy

Question

A velocity filter uses the properties of electric and magnetic fields to select charged particles that are moving with a specific velocity. Charged particles with varying speeds are directed into the filter as shown in figure. The filter consists of an electric field E and a magnetic field B, each of constant magnitude, directed perpendicular to each other as shown. The particles that move straight through the filter with their direction unaltered by the fields have the specific filter speed, V subscript 0 end subscript . Those with speeds to V subscript 0 end subscript may experience sufficiently little deflection that they also enter the detector.

The charged particle will experience a force due to the electric field given by the relationship stack F with rightwards arrow on top equals q stack E with bar on top where q is the charge of the particle and stack E with rightwards arrow on top is the electric field. The moving particle will also experience a force due to the magnetic field. This force acts to oppose the force due to the electric field. The strength of the force due to the magnetic field is given by the relationship stack F with rightwards arrow on top equals q left parenthesis stack v with bar on top cross times stack B with rightwards arrow on top right parenthesis where q is the charge of the particle, v rho is the speed of the particle, and stack B with bar on top is the magnetic field strength. When the forces due to the two fields are equal and opposite, the net force on the particle will be zero, and the particle will pass through the filter with its path unaltered. The electric and magnetic field strengths can be adjusted to choose the specific velocity to be filtered. The effects of gravity can be neglected.
The electric and magnetic fields in the filter of figure are adjusted to detect particles with positive charge q of a certain speed, V subscript 0 end subscript . Which of the following expressions is equal to this speed ?

  1. B/(q2E)    
  2. E/(q2B)    
  3. B/E    
  4. E/B    

The correct answer is: E/B

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