Question

A proton moving with velocity $v$ is acted upon by electric field $E$ and magnetic field $B$. The proton will move undetected, if

• A. E is perpendicular to B
• B. E is parallel to v and perpendicular to B
• C. E, B and v are mutually perpendicular and $ v=\frac{E}{B} $
• D. E and B both are parallel to v

Answer 1

Answer: (C)

If magnetic field $B$, and electric field $E$ are perpendicular to the direction of motion of proton, then proton will move without any deflection.
So, magnetic force = electric force. $e v B=e E$
$\therefore v=\frac{E}{B}$
$\therefore E , B$ and $v$ are mutually perpendicular and $v=E / B$