The force on a charged particle due to electric and magnetic fields is given by `vecF=qvecE+qvecv+vecB`. 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?

Explanation

Let
`vecE=Ehati`
`vecB=Bhatj`
And `vecv=v_(x)hati+v_(y)hatj+u_(z)hatk`
Net force acting on the particle can be written as follows:
`vecf=qEhati+q(v_(x)hatj+v_(z)hatk)xxB hatj`
`rArrvecF=qEhati+qv_(x)Bhatk-qv_(z)Bhati`
`rArr vecF=q(E-Bv_(z)hati+qv_(x)Bhatk)`
For force be become zero, individual components must be zero .
`F=0rArrv_(z)=E//B,v_(x)=0 and v_(y)` can have any value .
We need minimum possible speed, so we shall assume `v_(y)=0,` hance minimum possible speed to have net force zero is `E//B` along Z-axis.