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A charged particle is introduced at the origin x=0, y=0, z=0 with a given initial...

A charged particle is introduced at the origin x=0, y=0, z=0 with a given initial velocity →v . A uniform electric field →E  and a uniform magnetic field →B exist everywhere. The velocity →v , electric field →E  and a uniform magnetic field →B are given in the columns below
Column 1 Column 2 Column 3
1. Electron with  â†’v=2E0B0ˆx  (i) →E=E0ˆz (P)  â†’B=-B0ˆx
2. Electron with  â†’v=E0B0ˆy (ii)  â†’E=-E0ˆy (Q)  â†’B=B0ˆx
3.Proton with →v =0 (iii)  â†’E=-E0ˆx (R)  â†’B=-B0ˆy
4. Proton with  â†’v=2E0B0ˆx (iv)  â†’E=E0ˆx (S)  â†’B=-B0ˆz
In which case will the particle move in a straight line with a constant velocity?
(2),(iii)(S)
(4),(i)(S)
(3),(ii)(R)
(3),(iii)(P)
Solution:
Given: A charged particle is introduced at the origin (x=0,y=0,z=0). initial velocity =→v,
uniform electric field →E.
uniform magnetic field →B.
Also the values are given the table.
we need to find the cases where the particle will move in a straight line with constant velocity.
To move a particle with constant velocity;
Fnet =0,
⇒ The electric force = magnetic fore e.
qE=qvB.E=vB.
Now checking the options.
 A) (II) (iii) (s).  (II) =→v=E0B0ˆy (iii) =→E=−E0ˆx(s)=→B=B0ˆZ−E0ˆx=E0^BOˆy(BOˆz)
∴ (II) (iii) (s) is the correct option