A velocity filter uses the properties of electric and magnetic field to select particles that are moving with a specifice velocity. Charged particles with varying speeds are directed into the filter as shown. The filter consistt of an electric field E and a magnetic field B, each of constant magnitude, directed perpendicular to each other as shown, The charge particles will experience a force due to electric field given by F = qE. If positively charged particles are used, this force is towards right.

The moving particle will also experience a force due to magnetic field given by `F = qvB`. When forces due to the two fields are of equal magnitude, the net force on the particle will be zero, the particle will pass through centre with its path unaltered. The electric and magnetic fields can be adjusted t choose the specific velocity to be filtered. The efect of gravity can be neglected.
The electric and magnetic fields are adjusted to detect particles with positive charge q of certain speed `v_(0)`. which of the following expressions is equal to this speed?

Options

A. it would not work with negatively charged particles.
B. wider the detector entrance, the narrower the range of speed detected.
C. greater the distance d, the narrower the range of speed detected.
D. The detector may not detect a charged particles with desired filter speed if its charge is too high.

Answer

C

Explanation

Greater the distance d, larger would be the deviation produced in the path. Hence the particle will be unable to enter the detector for greater distance d, thus narrowing the range of speeds detected.