Question

In the following diagram, which particle has highest $e/m$ value?

• A. A
• B. B
• C. C
• D. D

Answer 1

The correct option is D D

Let us assume, if charged particles be moving with velocity V and its charge is q and mass m, then passing through electric field E, force acting is as:

$F=qE$

$⟹ma=qE$

$⟹a=\frac{q}{m}E$

Using,

$S=ut+\frac{1}{2}a{t}^2$

$⟹S=0+\frac{1}{2}\frac{qE}{m}{t}^2$

$=\frac{1}{2}\left(\frac{q}{m}\right)E(\frac{x}{v}{)}^2$

Where x is displacement

$⟹S=\frac{1}{2}\frac{q}{m}E(\frac{x}{v}{)}^2$

$⟹x^2=\frac{2m{v}^2}{qE}y$

$⟹x^2=ky;k=\frac{2m{v}^2}{qE}$

Thus if q is perpendicular, ti experiences force and follows parabolic path and largest derivation of D is seen,thus $\frac{e}{m}$ is max.