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.
If the filter is set to detect particles of speed `v_(0)`, which one of the following diagrams best illustrates how the magnitude of the particle acceleration (a) depends on velocity v?

Options

A.
B.
C.
D.

Answer

A

Explanation

For `v=0, a=(qE)/(m)`
for `v=v_(0), a=(qE-qvB)/(m)`
or `a=(-qB)/(m)v+(qE)/(m)(y=-mx+c)`
for `v=v_(0), a=0`
for `vgtv_(0) =(qBv)/(m)-(qE)/(m)(y=mx-c)`
hence graph (a) is correct.