Question

A proton moves in the positive $z-$direction after being accelerated from rest through a potential difference $V$. The proton then passes through a region with a uniform electric field $E$ in the positive x-direction and a uniform magnetic field $B$ in the positive $y-$ direction, but the proton's trajectory is not affected. If the experiment were repeated using a potential difference of $2V$, the proton would then be

• A. deflected in positive $x-$direction
• B. deflected in negative $x-$direction
• C. deflected in positive $y-$direction
• D. deflected in negative $y-$direction

Answer 1

The correct option is B deflected in negative $x-$direction

Since the magnetic field is in +y and velocity of proton is in +z, using $F=q\overrightarrow{v}\times \overrightarrow{B}$ the magnetic force is in -x direction which cancels the electric force (in +x) direction due to the correct velocity ( which we get from the relation $vB=E$).
Increasing the potential difference increases velocity increasing magnetic force but unaffecting electric force.