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

Question

Figure shows tracks of three charged particles crossing a uniform electrostatic field with same velocities along horizontal. Which particle has the highest charge to mass ratio? (A) 1 (B) 2 (C) 3 (D) cannot be calculated

Tardigrade Admin · Accepted Answer

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 particle, 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 charged particle along the vertical,

y = u t + \frac{1}{2} a t^{2}

Now, the initial velocity of the charged particle along vertical is zero. If

e

is charge on a particte and

m

is its mass, then acceleration produced in its path,

a = \frac{e E}{m}

∴ y = 0 \times t + \frac{1}{2} \frac{e E}{m} t^{2} = \frac{1}{2} \frac{e E}{m} t^{2}

As

E

and

t

are same for all the charged particles, it follows that

\frac{e}{m} \propto y

Since the charged particle 3 suffers maximum deflection along vertical, its charge to mass ratio is highest.

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

1

2

3

cannot be calculated