The force on a charged particle due to electric and magnetic fields is given by `vecF=qvecE+qvecvXvecB`. Suppose `vecE` is along the X-axis and `vecB` along the Y-axis. In what direction and with what minimum speed v should a positively charged particle be sent so that the net force on it is zero?

Answer

A, B, D

Explanation

Given `vecF`=`qvecE`+`q(vecvxxvecB`)=0

rarr E=-(vecvxxvecB)`
So the direction of `vxxB` should be opposite to the direction of `vecE. Hence vecv` should be in the +e yz-plane.
Again
`e=v B sin theta, rarr v=E/B sin theta` For v to be minimum
`theta = 90^0 and s v_(mn)=E/B`
So, the partilce must be projected at minimum speed of `E/B` along \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'-\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\' ve z- axis `(theta =90^0) as shown in the figure so that the force is zero.