Motion of charged particle in uniform electric field

Edited By Vishal kumar | Updated on Jul 02, 2025 05:51 PM IST

Imagine you're holding a small ball in your hand and then release it. Gravity pulls it straight down, causing it to accelerate towards the ground. Now, picture a charged particle, like an electron, placed in a uniform electric field. Instead of gravity, the electric field exerts a force on the particle, causing it to move.

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The Motion of Charged Particles in a Uniform Electric Field
Solved Examples Based on Motion of Charged Particle in the Uniform Electric Field
Summary

Motion of charged particle in uniform electric field

In a uniform electric field, the force acting on a charged particle is constant, meaning the particle will experience uniform acceleration, much like the ball in free fall. The direction of this acceleration depends on the charge of the particle: positive charges accelerate in the direction of the electric field, while negative charges accelerate in the opposite direction. This concept is fundamental in understanding the behaviour of charged particles in various environments, such as in cathode ray tubes, particle accelerators, and even in the basic operation of electronic devices. In this article, we'll explain the details of how charged particles move in uniform electric fields and explore some real-world examples to illustrate this phenomenon.

The Motion of Charged Particles in a Uniform Electric Field

Whenever a charge is placed in an electric field, it will experience an electric force. There is an assumption that this whole system is placed in a gravity-free space. For this condition, electrical force is the only force acting on the particle. This net force will cause the particle to accelerate according to Newton's second law of motion. So we can write

F→e=qE→=ma→

Acceleration will be constant if the Electric field is uniform and a→=qE→m . The direction of acceleration or motion of a charged particle depends on its nature. If the charged particle is of positive nature then it will move or accelerate in the direction of the electric field. But in the case of the negatively charged particle, its motion or acceleration is in the opposite direction of the electric field. Here we can use the kinematic equation of motion since the acceleration is constant.

Solved Examples Based on Motion of Charged Particle in the Uniform Electric Field

Example 1: An electron having charge ‘e’ and mass ‘m’ is moving in a uniform electric field E. Its acceleration will be :

1) e2m
2) E2em
3) Eem
4) mEe

Solution:

When charged Particle is at rest in a uniform field

Force and acceleration

F=QEa=QEm
wherein
m - mass
Q - charge
E - Electric field strength
a=Fm=eEm

Hence, the answer is the option (3).

Example 2: The acceleration of an electron in an electric field of magnitude 50 V/cm, if the e/m value of the electron is 1.76×1011C/kg, is
1) 8.8×1014 m/s2
2) 6.2×1013 m/s2
3) 5.4×1012 m/s2
4) Zero

Solution:

a=eEm⇒a=1.76×1011×50×102=8.8×1014 m/s2

Hence, the answer is the option (1).

Example 3: An electron moving with the speed of m/s is shot parallel to the electric field of intensity. The field is responsible for the retardation of the motion of electrons. Now evaluate the distance travelled by the electron before coming to rest for an instant (mass of charge =1.6×10−19C).
1) 7 m
2) 0.7 mm
3) 7 cm
4) 0.7 cm

Solution:

When Charged Particle at rest in uniform field -

Force and acceleration

F=QEa=QEm - wherein m - mass Q - charge E - Electric field strength. Electric force qE=ma⇒a=QEm∴a=1.6×10−19×1×1039×10−31=1.69×1015u=5×106 and v=0∴ from v2=u2−2a s⇒s=u22a∴ Distance s=(5×106)2×92×1.6×1015=7 cm( approx )

Hence, the answer is the option (3).

Example 4: An electron (mass =9.1×10−31 kg and charge = 1.6×10−19C ) is sent in an electric field of intensity 1×106 V/m How long would it take for the electron, starting from rest, to attain one-tenth the velocity of light?
1) 1.7×10−12sec
2) 1.7×10−6sec
3) 1.7×10−8sec
4) 1.7×10−10secSolution

When charged Particle is at rest in a uniform field

Velocity -

v=QEtm=2QΔVm
wherein
ΔV= Potential difference.

By using

v=QEtm⇒110×3×108=1.6×10−19×106×t9.1×10−31⇒t=1.7×10−10s

Hence, the answer is the option (4).

Example 5: Particle A has a charge of +q and particle B has a charge of +4q with each of them having the same mass m. When allowed to fall from rest through the same electrical potential difference, the ratio of their speeds vAvB will become:

1) 2:1

2) 1:2

3) 1:4

4) 4:1

Solution:

We know that kinetic energy

K=12mv2=QV

Since m and V are the same so,
v2∝Q⇒vAvB=QAQB=q4q=12

Hence, the answer is the option (2).

Summary

If a charged particle is placed into a uniform electric field it will be subjected to a continuous force caused solely by this field. Consequently, a positively charged one will move in the direction of an electric field line, whereas a negatively charged one moves oppositely. Equations of motion for constant acceleration can be utilized in order to determine the direction and speed of these particles according to the time factor.

Frequently Asked Questions (FAQs)

1. How can you determine the charge of a particle based on its motion in a known electric field?

To determine the charge of a particle based on its motion in a known electric field, you can measure its acceleration and use the equation F = qE = ma, where F is the force, q is the charge, E is the known electric field strength, m is the particle's mass, and a is its measured acceleration. Rearranging this equation gives q = ma/E, allowing you to calculate the charge if you know the particle's mass and can measure its acceleration.

2. What is the difference between the motion of a charged particle in a gravitational field versus an electric field?

While both gravitational and electric fields can cause acceleration of particles, there are key differences:

3. What determines the trajectory of a charged particle in a uniform electric field?

The trajectory of a charged particle in a uniform electric field is determined by the particle's initial velocity, its charge-to-mass ratio, and the strength and direction of the electric field. The field exerts a constant force on the particle, causing it to accelerate in the direction of the field if positively charged, or opposite to the field if negatively charged.

4. How does the motion of a charged particle differ when it enters an electric field parallel vs. perpendicular to its initial velocity?

When a charged particle enters an electric field parallel to its initial velocity, it experiences constant acceleration along its path, resulting in uniformly accelerated motion. When entering perpendicular to its initial velocity, the particle follows a parabolic path, similar to projectile motion, as the field provides constant acceleration perpendicular to the initial velocity.

5. Why do electrons and protons move in opposite directions in a uniform electric field?

Electrons and protons move in opposite directions in a uniform electric field because they have opposite charges. The electric field exerts a force on charged particles in the direction of the field for positive charges (protons) and opposite to the field for negative charges (electrons). This results in acceleration in opposite directions for the two particles.

6. Can a charged particle remain stationary in a uniform electric field?

Yes, a charged particle can remain stationary in a uniform electric field if there is another force exactly balancing the electric force. For example, in Millikan's oil drop experiment, charged oil droplets can be suspended in air when the electric force upward exactly balances the gravitational force downward.

7. How does the acceleration of a charged particle in a uniform electric field depend on its mass?

The acceleration of a charged particle in a uniform electric field is inversely proportional to its mass. This relationship is described by the equation a = (qE)/m, where a is acceleration, q is charge, E is electric field strength, and m is mass. Particles with larger mass experience less acceleration for the same electric force.

8. How does the motion of charged particles in non-uniform electric fields differ from their motion in uniform fields?

In non-uniform electric fields, the motion of charged particles is more complex than in uniform fields:

9. What is the shape of the path followed by a charged particle entering a uniform electric field at an angle?

When a charged particle enters a uniform electric field at an angle (neither parallel nor perpendicular), it follows a parabolic path. This is because the particle experiences constant acceleration in the direction of the field (or opposite to it, depending on the charge), while maintaining its initial velocity component perpendicular to the field.

10. How does the kinetic energy of a charged particle change as it moves through a uniform electric field?

The kinetic energy of a charged particle changes as it moves through a uniform electric field due to the work done by the electric force. If the particle moves in the direction of the force (e.g., a positive charge moving in the field direction), its kinetic energy increases. If it moves against the force, its kinetic energy decreases. The change in kinetic energy is equal to the work done by the electric field.

11. What is the significance of the charge-to-mass ratio in determining a particle's motion in an electric field?

The charge-to-mass ratio (q/m) is crucial in determining a particle's motion in an electric field because it directly affects the acceleration experienced by the particle. Particles with a higher charge-to-mass ratio will experience greater acceleration for a given electric field strength, as described by the equation a = (qE)/m. This ratio is particularly important in applications like mass spectrometry.

12. How can you use the motion of charged particles in electric fields to separate isotopes?

Isotope separation using electric fields relies on the fact that isotopes of an element have the same charge but different masses. When ionized isotopes are accelerated through an electric field, they gain the same energy but achieve different velocities due to their mass differences. This velocity difference can be exploited in devices like mass spectrometers to separate and identify isotopes.

13. What is the difference between uniform and non-uniform electric fields in terms of particle motion?

In a uniform electric field, the force on a charged particle is constant in magnitude and direction, resulting in constant acceleration and predictable trajectories like parabolas or straight lines. In non-uniform fields, the force varies with position, leading to more complex, often curved trajectories that can be difficult to predict without detailed analysis or simulation.

14. How does air resistance affect the motion of charged particles in an electric field?

Air resistance introduces a drag force that opposes the motion of charged particles in an electric field. This force increases with velocity and can cause the particle to reach a terminal velocity where the drag force balances the electric force. Air resistance tends to make the trajectory of the particle more complex and can significantly alter its motion, especially for lighter particles or at higher velocities.

15. What is meant by the "deflection sensitivity" of a charged particle in an electric field?

Deflection sensitivity refers to how easily a charged particle's path can be altered by an electric field. It is typically higher for particles with a larger charge-to-mass ratio, as they experience greater acceleration for a given field strength. Deflection sensitivity is important in applications like cathode ray tubes and electron microscopes, where precise control of particle trajectories is crucial.

16. What is the principle behind the operation of an electrostatic precipitator?

An electrostatic precipitator uses the motion of charged particles in an electric field to remove particulates from gases. It works by first charging the particles using a corona discharge, then passing them through a strong electric field. The charged particles are attracted to oppositely charged collection plates, where they are deposited and removed from the gas stream. This principle relies on the predictable motion of charged particles in electric fields.

17. How does the initial velocity of a charged particle affect its trajectory in a uniform electric field?

The initial velocity of a charged particle affects its trajectory in a uniform electric field by determining the starting conditions for its motion. A higher initial velocity component parallel to the field will result in the particle traveling further before being deflected. A higher perpendicular component will lead to a wider parabolic path. The overall trajectory is a combination of the particle's initial motion and the acceleration caused by the electric field.

18. What is the relationship between electric potential energy and kinetic energy for a charged particle moving in an electric field?

For a charged particle moving in an electric field, the sum of its electric potential energy and kinetic energy remains constant (assuming no other forces are present). As the particle moves in the direction of the electric force, its electric potential energy decreases while its kinetic energy increases by an equal amount. This is an application of the conservation of energy principle.

19. How can the motion of charged particles in electric fields be used to create images in a television or computer monitor?

In cathode ray tube (CRT) displays, electrons are emitted from a heated cathode and accelerated by an electric field. They are then deflected by electric (or magnetic) fields to scan across a phosphor screen, creating images. The precise control of the electron beam's motion using electric fields allows for the creation of detailed images by selectively exciting different areas of the phosphor screen.

20. What factors determine the time of flight of a charged particle in a uniform electric field?

The time of flight of a charged particle in a uniform electric field depends on several factors:

21. How does the concept of electric field lines relate to the motion of charged particles?

Electric field lines provide a visual representation of the direction and strength of an electric field. Charged particles tend to move along these field lines: positive charges move in the direction of the field lines, while negative charges move opposite to them. The density of field lines indicates field strength, with denser lines representing stronger fields where particles would experience greater acceleration.

22. What is the significance of the "critical velocity" for a charged particle entering an electric field?

The critical velocity is the minimum initial velocity a charged particle needs to escape a region of electric field without being turned back. It's particularly relevant for particles entering a field perpendicular to their initial motion. If the particle's initial velocity is below the critical velocity, it will eventually reverse direction and exit the field on the same side it entered. This concept is important in understanding particle confinement and escape in various physical systems.

23. How does the motion of charged particles in electric fields relate to the concept of electrical work?

The motion of charged particles in electric fields directly relates to electrical work. As a charged particle moves in an electric field, work is done on it by the electric force. This work equals the change in the particle's kinetic energy. The work done is positive if the particle moves in the direction of the electric force (increasing its kinetic energy) and negative if it moves against the force (decreasing its kinetic energy). This relationship is expressed as W = qEd cos θ, where W is work, q is charge, E is field strength, d is displacement, and θ is the angle between the field and displacement.

24. How can the motion of charged particles in electric fields be used to measure the charge-to-mass ratio of electrons?

The charge-to-mass ratio of electrons can be measured using their motion in electric and magnetic fields. In a classic experiment, electrons are accelerated by an electric field and then deflected by a magnetic field. By measuring the deflection and knowing the field strengths, the charge-to-mass ratio can be calculated. This method, first used by J.J. Thomson, was crucial in the discovery of the electron and remains an important technique in particle physics.

25. What is the principle behind the operation of an ink-jet printer in terms of charged particle motion?

Ink-jet printers use the controlled motion of charged ink droplets in an electric field. The ink is given an electric charge as it's ejected from the nozzle. It then passes through an electric field that can be varied to deflect the droplets. By precisely controlling this deflection, the printer can accurately position ink droplets on the paper to form text and images. This application demonstrates the practical use of charged particle motion in everyday technology.

26. How does the motion of charged particles in an electric field relate to the concept of electric current?

Electric current is fundamentally the flow of charged particles. In a conductor subjected to an electric field, free electrons (negatively charged) move opposite to the field direction, constituting an electric current. The motion of these charged particles is governed by the principles we've discussed: they accelerate due to the electric force, their velocity is influenced by collisions with the lattice, and their overall drift gives rise to the macroscopic phenomenon of current flow.

27. What is the role of electric fields in particle accelerators?

Electric fields play a crucial role in particle accelerators by providing the energy to accelerate charged particles to high velocities. In linear accelerators, particles pass through a series of electric fields that switch polarity at the right moment to continually accelerate the particles. In circular accelerators like synchrotrons, electric fields are used to increase particle energy while magnetic fields bend the particle path into a circle. The precise control of particle motion using electric fields is essential for achieving the high energies needed for particle physics experiments.

28. How does the motion of charged particles in electric fields contribute to the aurora borealis (Northern Lights)?

The aurora borealis is caused by the motion of charged particles (mainly electrons and protons) from the solar wind entering Earth's magnetosphere. These particles are guided by Earth's magnetic field towards the polar regions, where they interact with the upper atmosphere. As they descend, they encounter increasing electric fields due to the potential difference between the ionosphere and the ground. These fields accelerate the particles, causing them to collide with atmospheric molecules and atoms, exciting them to higher energy states. When these excited particles return to their ground state, they emit light, creating the spectacular auroral displays.

29. What is the principle behind electrostatic painting, and how does it relate to charged particle motion?

Electrostatic painting utilizes the motion of charged particles in an electric field to efficiently coat objects. The paint particles are given an electric charge as they're sprayed, while the object to be painted is grounded (or given an opposite charge). The electric field between the spray nozzle and the object causes the charged paint particles to be attracted to the object's surface. This results in a more even coating with less overspray, as the paint particles actively seek out the surface rather than simply being sprayed in its general direction. The motion of the charged paint particles follows the principles of charged particle motion in electric fields, with their trajectories influenced by the field strength and geometry.

30. How does the concept of equipotential surfaces relate to the motion of charged particles in electric fields?

Equipotential surfaces are imaginary surfaces where the electric potential is constant. Charged particles moving along these surfaces do not experience any change in their electric potential energy. The motion of a charged particle crossing equipotential surfaces is key to understanding its energy changes:

31. What is the significance of the "electron volt" as a unit of energy in the context of charged particle motion?

The electron volt (eV) is a unit of energy commonly used in atomic and particle physics. One electron volt is defined as the amount of kinetic energy gained by an electron when it is accelerated through a potential difference of one volt. This unit is particularly useful when discussing the motion of charged particles in electric fields because:

32. What is the principle behind the mass spectrometer, and how does it utilize the motion of charged particles in electric fields?

A mass spectrometer uses the motion of charged particles in electric and magnetic fields to separate ions based on their mass-to-charge ratio. The basic principle involves:

33. How does the presence of other charged particles affect the motion of a single charged particle in an electric field?

The presence of other charged particles can significantly affect the motion of a single charged particle in an electric field: