The Trajectory Of Particle In Electric Field

The entire world is made up of charged particles. It is the interaction between charged particles that leads us to observe all the phenomena in our universe. But what is a charged particle? All entities consist of subatomic particles namely, electrons, neutrons and protons. When there is a disbalance in the amount of neutrons, electrons and protons present in an atom or a particle, then that particle is said to have a charge on them. Such particles are called charged particles.

Charged particles behave in a special manner when subjected to different types of environment. Of all these environments, the interactions of a charged particle in an electric field is of prime importance. This is because electric fields are used in various applications like particle accelerators etc.

What is an Electric Field?

In the universe, the presence of a particle influences other entities around it. Placing a charged particle in space creates an influence around it. When another charged particle is introduced to this space, a certain force gets applied on it. The reason behind this force lies in the fact that the particle is brought into the field of another charged particle.

The area around the charged particle due to which a second charged particle will feel a force when present in that field is called the electric field of the particle. Electric field is a quantity that is associated with a point in space, around which an electric charge is present. If given the electric field at a point in space, one can accurately calculate the force that will be applied on a charge at that point without having knowledge of what is the source charge responsible for the electric field.

Trajectory of Particle in Electric Field

A charged particle can enter an electric field in two different manners. Either it can enter the field in a direction that is perpendicular to the direction of the electric field or it can enter the electric field such that it is along the direction of the electric field.

When a charged particle enters the electric field in a perpendicular direction

An electric field can be imagined as a wave of water that is constantly flowing in one direction. When something enters the water such that it is perpendicular to its direction of flow, it receives a huge impact from the force of the water. Similarly, when a charged particle enters the electric field perpendicular to it, then it receives a force that can be towards the source of the electric field or away from it, depending on the nature of the charge.

This causes the path of the charged particle to be curved. Since the force is acting perpendicular to the motion of the charge, the change in trajectory due to the applied force results in the path of the charged particle becoming a parabola. When the charge is positive, the parabolic trajectory is curved towards the electric field. On the contrary when the charge is negative, the parabolic trajectory is curved away from the electric field.

When a charged particle enters the electric field in the direction of the electric field

The charged particle enters the electric field in the easiest manner when it enters along the direction of the electric field. But based on the polarity of the charge, it will either get repelled or attracted. However for both the charges their trajectory in the electric field will be a straight line. This means if the charge is positive, then the trajectory will be a straight line away from the positive end of the source charge. On the contrary, if the charge is negative, then the trajectory will be a straight line towards the positive end of the source charge.

Solved Examples of the trajectory of a particle in an electric field

Ques. Show that the trajectory followed by a charged particle when it enters perpendicular to an electric field is a parabola.

Ans.

Let E be the electric field that the charged particle enters. The charge on the particle is qo and let m denote the mass of the charge. Then we can say that, when the charged particle enters the electric field it experiences a force that is given by;

F=qoE

Since a force is applied on the charge it will also gain some acceleration that is given by;

F =ma ⇒ a=F/m

Putting the value of F and the mass of the particle m, we get;

a=qoE/m

The distance that is travelled by the charged particle inside the electric field is given as;

t=x/v

Let us assume that when the charged particle enters the electric field, the initial velocity was zero, this means that the distance that was covered by the charge in the electric field can be given as;

y=1/2at2

y=1/2qoE/m(x/v)2

y=qoE / 2mv2 *x2

y=kx2 where k=qoE/2mv2 and is a constant.

Therefore we can say

y is directly proportional to x2 and hence the trajectory of the charged particle is a parabola.

Conclusion

Charged particles behave in a special manner when subjected to different types of environment. Of all these environments, the interactions of a charged particle in an electric field is of prime importance. This is because electric fields are used in various applications like particle accelerators etc.

When a charged particle enters the electric field perpendicular to it, then it receives a force that can be towards the source of the electric field or away from it, depending on the nature of the charge. Depending on the nature of the charge, it will either get repelled or attracted.