Question

Write the expression for the force,`vecF` acting on a charged particle of charge ‘q’, moving with a velocity `vecV` in the presence of both electric field `vecF`and magnetic field `vecB` . Obtain the condition under which the particle moves undeflected through the fields.

Answer 1

 Force `vecF` acting on a charge ‘q’ moving with velocity `vecV`  in the presence of both electric field `vecE`  and magnetic field `vecB` ,

`vecF =qvecE +q(vecVxxvecB)`

Consider a region in which magnetic field, electric field and velocity of charge particle are perpendicular to each other.

To move charge particle undeflected the net force acting on the particle must be zero i.e. The electric force must be equal and opposite to the magnetic force.

qE = qvB

`V=E/B`

The direction of electric and magnetic forces are in opposite direction. Their magnitudes are in such a way they cancel out each other to give net force zero so that the charge particle does not deflect.