Question

Figure 1.33 shows tracks of three charged particles in a uniformelectrostatic field. Give the signs of the three charges. Which particlehas the highest charge to mass ratio?

Answer 1

We know that, charges of same type repel each other and opposite charges attract each other.

From the given figure, we can observe that the particle (1) and particle (2) both moved towards the positive charge. Thus particle (1) and (2) are negatively charged.

Since, particle (3) moved towards the negative charge, hence particle (3) is positively charged.

The force on a charged particle in electric field is given as,

F=qE(1)

Where, F is force, q is the charge and E is the uniform electric field.

The force on a particle is also given as,

F=ma (2)

Where, m is the mass of the particle and a is the acceleration of the particle.

From equation (1) and (2), we get

pE=ma a= qE m

Deflection of the particle is given as,

s=vt+ 1 2 a t 2 (3)

Where, s is the deflection and t is the time taken.

By substituting the value of a in the above equation (3), we get

s=vt+ 1 2 ( qE m ) t 2

Since, the particle enters the field with the same horizontal velocity and they remains in the field for the same time, thus E, t and v are constant for the above expression. Thus,

s∝ q m

Since, the deflection of the particle (3) is maximum, thus particle (3) will have the highest charge to mass ratio.