Write the expression for the force `vecF` acting on a particle of charge q moving with a velocity `vecv` in the prensnece of both electric field `vecE` and magnetic field `vecB`. Obtain the condition under which the particle moves undeflected through the fields.

Explanation

1st Part : Force
`vecF= vecF_(e) +vecF_(m)= qvecE+ qvecvxx vecB=q(vecE+vecv xx vecB)`
2nd Part : The required condition is either, `vecF=0`, i., ono resultant force acts on the particle. In that case, `vecE=-qvecvxx vecB`.
or, `vecE and vecB` are both along the direction of velocity of the particle, of motion produces a constant acceleration without any deflection.