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A charged particle (electron or proton) ...

A charged particle (electron or proton) is introduced at the origin `(x = 0, y = 0, z = 0`) with a given initial velocity `vecv`. A uniform electric field `vecE` and a uniform magnetic field `vecB` exist everywhere. The velocity `vecv`, electric field `vecE` and magnetic field `vecB` are given in columns 1,2 and 3 respectively. The quantities `E_(0), B_(0)` are positive in magnitude.
`{:("Column-1","Column-2","Column-3"),("Electron with" vecv=2(E_(0))/(B_(0))hatx, (i)vecE=E_(0)vecz,(P) vecB=-B_(0)hatx),((II)"Electron with" vecv=(E_(0))/(B_(0))haty,(ii)vecE=-E_(0)hatx,(Q)vecB=B_(0)hatx),((VI)"Proton with" vecv=0,(iii)vecE=-E_(0)hatx,(R)vecB=B_(0)haty),((VI)"Proton with" vecv=2(E_(0))/(B_(0))hatx,(iv)vecE=E_(0)hatx,(S)vecB=B_(0)hat2):}`
In which case would the particle move in a straight line along the negative direction of y-axis (i.e., move along `haty)`

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A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0 ) with a given initial velocity vecv . A uniform electric field vecE and a uniform magnetic field vecB exist everywhere. The velocity vecv , electric field vecE and magnetic field vecB are given in columns 1,2 and 3 respectively. The quantities E_(0), B_(0) are positive in magnitude. {:("Column-1","Column-2","Column-3"),("Electron with" vecv=2(E_(0))/(B_(0))hatx, (i)vecE=E_(0)vecz,(P) vecB=-B_(0)hatx),((II)"Electron with" vecv=(E_(0))/(B_(0))haty,(ii)vecE=-E_(0)hatx,(Q)vecB=B_(0)hatx),((VI)"Proton with" vecv=0,(iii)vecE=-E_(0)hatx,(R)vecB=B_(0)haty),((VI)"Proton with" vecv=2(E_(0))/(B_(0))hatx,(iv)vecE=E_(0)hatx,(S)vecB=B_(0)hat2):} In which case will the particle move in a straight line with constant velocity ?

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