Lorentz Force: Definition, Formula, Derivation and Examples (2024)

Lorentz force refers to a combination of magnetic and electric force that acts on a point charge due to the presence of electromagnetic fields. Furthermore, the Lorentz force is also known by experts as the electromagnetic force.

Introduction to Lorentz Force

Experts define Lorentz force as the combination of the magnetic and electric force. Furthermore, this force acts on a point charge due to electromagnetic field.

Lorentz force explains the equations of mathematical nature along with the physical importance of forces which act on the charged particles. Moreover, these particles travel through space which contains electric and magnetic field.

Lorentz Force: Definition, Formula, Derivation and Examples (1)

How do we Measure Lorentz Force?

Lorentz force on a moving charge that is present in a B Field

Lorentz force happens when the movement of a charged particle takes place through a magnetic field and cuts through field lines in the process. This force acts at right angles to both the particle velocity, v, and the magnetic field, B.

This force’s direction in various situations is dependent on the direction of the velocity of the particle and the magnetic field as well as the sign of the particle’s charge. There are two ways of remembering the direction of this force and both these ways are variants of the “left-hand rule”.

Thumb,First finger and Second finger:

These are held at right angles to each other and a rotation takes place so that:

  • thepointing of the First finger is in the direction of the MagneticField
  • furthermore, the pointing of the Second finger is in the direction of theCurrent
  • the pointing of the Thumb’s direction is in the direction that theMotion would tend to if the magnetic force in case is the only force present.

There is an alternative way of remembering the left-hand rule that involves using the acronym “FBI” to label your fingers. As such, “I” refers to the middle finger, “F” refers to the thumb, and “B” refers to the first finger.

Holding these three fingers at right angles to each other would show the relationship between the directions of the current I, forceF, and magnetic fieldB.

Lorentz Force on a current-carrying wire that is present in a magnetic field:

A current refers to the movement of charged particles, so if a wire which has current is within amagnetic field, then all of the charged particles would be experiencing a Lorentz force.

So, one would need to find out the sum of the forces on the moving charged particles. This is because the sum of the forces on the moving charged particles would be equal to the overall force on the wire.

Lorentz Force by Making Use of Vector Notation

Usingvector notation, the force which acts on a moving charge,q,in a magnetic field, B​,is expressed as:

F​=qv​×B

In accordance with the rules of vector notation, this means thatF​should be at right angles to bothB​ and v and making use of the right-hand screw rule would provide us with the correct direction forF​.

The formula of Lorentz Force

F=q(E+v∗B)

Where,

  • F is the force whose effect takes place on the particle
  • q is the particle’s electric charge
  • v is the velocity
  • E refers to the external electric field
  • B is the magnetic field

Derivation of the Formula of Lorentz Force

Lorentz force on a moving charge that is present in a B Field

The size of the Lorentz Force is expressed as:

F=qvBsinθ

wheretheta,θ,refers to the angle between the velocity of the particle and the magnetic field. Furthermore, qrefers to the charge of the particle.

If the movement of the particle takes place in the direction of the magnetic field, without cutting across any field lines,theta, equals, 0,θ=0and there would be no Lorentz Force that acts on the particle.

If the particle is moving perpendicular to the magnetic field,sinθ=1, the particle will come undercircular motion with a radiusr. Furthermore, the determination of rcan take place by equating the centripetal force and the Lorentz force:

mv2/r ​= qvB

Lorentz Force on a current-carrying wire that is present in a magnetic field:

This is another way of Lorentz force derivation. ForNcharged particles, each with a chargeq and having a movement at the speedv. Furthermore, its movement takes place along a wire at an angletheta,θ,to a magnetic field of strengthB. Therefore, the total force on the wire would be:

F=NqvBsinθ

The expression of the magnitude of the current travelling down the wireI is as:

I=nAve

wheren happens to be the number density of free electrons in the wire. Moreover, Arefers to the wire’s cross-sectional area and v refers to the speed of the electrons along the wire. Also, the magnitude of an electron’s charge is e.

Thisgives:

v= I​/nAe.

Substituting this:

F= NqBIsinθ​/nAe

Finally, we get the equation for the magnitude of the force that acts on the wire:

F=BIlsinθ

Lorentz Force by Making Use of Vector Notation

It is possible to derive this force in vector form. So, the force that acts on a moving chargeq, in a magnetic field B,​can be expressed as:

F​=qv​×B

The expression of the Lorentz force on a current-carrying wire in a magnetic fieldB​can take place in vector notation as:

F​=I∫wiredl​×B

wheredl​happens to be an infinitesimal displacement that takes place along the wire. Furthermore, B​refers to the magnetic field at the relevant point. Also, the integral is taken over the wire’s entire length.

Adding the force which acts on a charged particle due to an electric field F​=qE​ would give a total Lorentz force on a particle of:

F​=q(E​+v​×B​)

FAQs on Lorentz Force

Question 1: What is meant by Lorentz force?

Answer 1: Lorentz force refers to a combination of magnetic and electric force that happens because of electromagnetic fields.

Question 2: Explain the importance of Lorentz law?

Answer 2: This force explains the mathematical equations in an appropriate manner. Furthermore, it explains the physical importance of forces that act on the charged particles.

Lorentz Force: Definition, Formula, Derivation and Examples (2024)

FAQs

Lorentz Force: Definition, Formula, Derivation and Examples? ›

Lorentz force, the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B. The entire electromagnetic force F on the charged particle is called the Lorentz force (after the Dutch physicist Hendrik A. Lorentz) and is given by F = qE + qv × B.

How to derive Lorentz force formula? ›

Derivation of Lorentz Force Law
  1. We begin with the assumption that a particle with rest mass m, charge q. and no velocity moves according to Newton's law (because it is at or nearly. ...
  2. system. ...
  3. + ...
  4. = γ ...
  5. . ...
  6. = qE∥. ...
  7. = q γ γ ( ⃗E⊥ + ⃗v c × ⃗B ) = q ( ⃗E⊥ + ⃗v c × ⃗B ) .
Mar 9, 2021

What is Lorentz force with example? ›

Lorentz force is defined as the combination of the magnetic and electric force on a point charge due to electromagnetic fields. It is used in electromagnetism and is also known as electromagnetic force. In the year 1895, Hendrik Lorentz derived the modern formula of Lorentz force.

What is the Lorentz equation statement? ›

F → E M = q ( E → + v → × B → ) . This is the Lorentz force equation, where F → E M stands for the electromagnetic force. Example 1: A charge of +q moves with velocity v → = x x ^ + y y ^ through a magnetic field defined by B → = x x ^ .

How to derive F qvB? ›

The magnitude of the Lorentz force F is F = qvB sinθ, where θ is the smallest angle between the directions of the vectors v and B. If v and B are parallel or anti-parallel to each other, then sinθ = 0 and F = 0. If v and B are perpendicular to each other, then sinθ = 1 and F has its maximum possible magnitude F = qvB.

How do you derive the Lorentz equation? ›

Lorentz Transformation Derivation
  1. S and S' = two inertial frames out of which S' is moving relative to S with v velocity along positive x-axis.
  2. At the beginning t = t' = 0.
  3. Origin O and O' will coincide.

What is the mathematical expression for Lorentz force? ›

Lorentz force, the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B. The entire electromagnetic force F on the charged particle is called the Lorentz force (after the Dutch physicist Hendrik A. Lorentz) and is given by F = qE + qv × B.

What is the right hand thumb rule for Lorentz force? ›

We can remember this diagram using the right-hand rule. If you point your pointer finger in the direction the positive charge is moving, and then your middle finger in the direction of the magnetic field, your thumb points in the direction of the magnetic force pushing on the moving charge.

What are the real life applications of Lorentz force? ›

The applications of Lorentz force are defined as follows:
  • It is used in the medical industry in the form of an instrument known as hydrophone.
  • It is also used as an ultrasound transducer in the medical field.
  • Lorentz Force is also used in Electrical Impedance Tomography which is an imaging technique.
Nov 14, 2023

What is the difference between Lorentz force and magnetic Lorentz force? ›

The term qE is called the electric force, while the term q(v × B) is called the magnetic force. According to some definitions, the term "Lorentz force" refers specifically to the formula for the magnetic force, with the total electromagnetic force (including the electric force) given some other (nonstandard) name.

What is the significance of the Lorentz force equation? ›

Experts define Lorentz force as the combination of the magnetic and electric force. Furthermore, this force acts on a point charge due to electromagnetic field. Lorentz force explains the equations of mathematical nature along with the physical importance of forces which act on the charged particles.

What is the standard form of the Lorentz equation? ›

The Lorentz force is the definition of these fields, and in F it is F = q(E + v × B) while in F′ it is F′ = q(E′ + v′ × B′).

Is Lorentz force a Maxwell equation? ›

It gives how E field and B affect charge, so it provides this direction of interaction E , B → Q \bold{E},\bold{B}\rightarrow Q E,B→Q. It's not a Maxwell's Equation because, unlike the other four, it doesn't describe electromagnetic field (or E and B).

How is force formula derived? ›

The formula for force states that the force is equal to mass that is multiplied by the acceleration. So, if we know the mass and the acceleration, we just have to multiply them together and then we will get the force.

What does Lorentz law state? ›

When a charged particle moves through a region in which both electric and magnetic fields are present, then the net force experienced by that charged particle is the sum of electrostatic force and magnetic force and is called the Lorentz force. Concept: Magnetic Force.

What is the direction of the Lorentz force? ›

The direction of Lorentz force is perpendicular to the direction of the moving charge and the magnetic field. The Lorentz force direction is well explained by using the Right-hand rule (Lorentz Force right-hand rule).

How do you derive the formula of force? ›

The second law of motion by Newton says that the force is equal to the change in momentum per change in the time. For a constant mass, force equals the mass times acceleration, i.e. F = m x a. If the time interval for the applied force increases, as a result, the value of the force applied decreases.

How do you derive electric force formula? ›

How do you find the electric force between two electrons? If the two electrons are at a distance of r then use the equation F=k*q*Q/r^2 and substitute the known electron's charge: q=Q=1.6x10^-19 C to find the electric force in terms of distance r. The further the electrons go apart the weaker the force is.

How do you derive impulse formula? ›

Momentum and Impulse

The units are Ns . The impulse of a force is I=Ft I = F t - when a constant force F acts for a time t . The units are Ns . The Impulse-Momentum Principle says I=mv−mu I = m v − m u which is final momentum - initial momentum so Impulse is the change in momentum.

How to derive F bil? ›

Derive F = BIL by starting with a single charge formula F = qvB and recognizing that current is simply I = Q/t.

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