Figure shows tracks of three charged particles crossing a uniform electrostatic field with same velocities along horizontal. Give the sign of the three charges. Which particle has the highest charge to mass ratio?

Options

A. 1
B. 2
C. 3
D. Can not be calculated

Answer

c

Explanation

Charge `1` and `2` are deflected towards the positive plate, hence they are negatively charged particles. On the other hand , charge `3` is positively charged particles as it gets deflected towards negative plate.

Since all the three charged particles are crossing the electric field with same velocities, they remain under the action of electric field `E`(say) for the same time `t`. The, deflection produced in the path of a charge particle along the vertical,
`y- ut+1/2at^(2)`
Now, the initial velocity of the charged particle along vertical is zero. If `e` is charge on a particle and `m` is its mass, then acceleration produced in its path,
`a=(eE)/(m)`
`:. y=0xxt+1/2(eE)/(m)t^(2)= 1/2(eE)/(m)t^(2)`
As `E` and `t` are same for all the charged particles, it follows that
`(e)/(m) prop y`
Since the charged particle `3` suffers maximum deflection along verticle, its charge to mass ratio is highest.