Lorentz Force: Definition, Formulas, and Example Problems

The Lorentz force was discovered by Herdik Anton Lorentz in 1853-1928. He is a scientist from the Netherlands who greatly contributed in the field of physics. The Lorentz force is actually a combination of electric and magnetic forces in an electromagnetic field.

The Lorentz force can arise due to the presence of an electric charge in a magnetic field. The Lorentz force has magnitude and also has direction. The direction of the Lorentz force uses the right-hand rule and is always perpendicular to the direction of the existing electric current and magnetic induction.

Biographies Hendrik Antoon Lorentz

Henry Anthony Lorentz.

The Lorentz force was discovered by Hendrik Anton Lorentz (1853-1928). He was a Dutch physicist who won the Nobel Prize for Physics together with Pieter Zeeman in 1902. He was born in Arnhem, Netherlands on July 18, 1853. As an adult, he studied at Leiden University.

Subsequently, at the age of 19 he returned to Arnhem and taught at one of the secondary schools there. While teaching, he prepared a doctoral thesis which expanded on James Clerk Maxwell’s theory of the electromagnet, which included details of the reflection and refraction of light.

In 1878, he became professor of theoretical physics at Leyden which was his first place of work. He lived there for 34 years, then moved to Haarlem. Lorentz continued his work to simplify Maxwell’s theory and introduce the idea that electromagnetic fields are generated by electric charges at the atomic level. He proposed that the emission of light by atoms and various optical phenomena could be traced to the motion and energy interactions of atoms.

In 1896, one of his students named Pieter Zeeman found that the spectral lines of atoms in a magnetic field split into several components with slightly different frequencies. This justified Lorentz’s work, for which they were both awarded the Nobel Prize in 1902.

In 1895, Lorentz devised a set of equations which transformed the electromagnetic quantity from one reference frame to another, moving relative to the first, although the importance of these discoveries was realized only 10 years later when Albert Einstein proposed his special theory of relativity.

Lorentz (and the Irish physicist GF Fitzgerald independently) proposed that the negative result of the Michelson-Morley experiment could be understood if the length in the direction of motion relative to the observer contracts. Subsequent experiments showed that although there was shrinkage, it was not due to any apparent cause in the results of Michelson and Edward Morley. The reason for this is that there is no “ether” that acts as a universal frame of reference.

Definition of Lorentz force

What is the Lorentz force? The Lorentz force is a force that comes from a combination of two forces. The two forces are the magnetic force and the electric force present in an electromagnetic field. This force comes from an electric charge that can move if an electric current is present in a magnetic field B. The presence of an electric force cannot be separated from an inventor.

The person who is credited with discovering this force is Hendrik Antoon Lorentz from 1853 to 1928. He is a physicist from the Netherlands and has won the Nobel Prize in Physics together with a man named Pieter Zeeman in 1902.

The name Hendrik Antoon Lorentz was later immortalized as a style he discovered and people know this style as the Lorentz style until now. From this style, electric motors are also found which function to drive tools such as blenders, fans, machines, washing machines, and so on.

Lorentz force formula

When there is a wire that is energized by an electric current of I and the wire is placed in the middle of a magnetic field, then a magnetic force will arise on the wire. By combining the magnetic force with the electric current, we can calculate how much force is on the wire, so the following formula appears:

Lorentz  = BI l sin α

Information:
Florentz = Lorenz force B = strong magnetic field current (Tesla) I = strong current flowing in the wire (amperes) I = length of wire (m) α = angle formed from B and I

Determining the Direction of the Lorentz Force

1. Lorentz force on a current-carrying wire

If the direction of the electric current is perpendicular to the direction of the magnetic field, the maximum magnetic force will occur (sin 90º = 1). In other words, so that the magnetic force can be maximally formed, the magnetic field must be conditioned perpendicular to the flowing electric current.

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Meanwhile, determining the direction of the Lorentz force can be through the hand rule as shown below:

For the first Lorentz style right hand rule using three fingers, namely:

  • Thumb = direction of electric current (I).
  • Index finger = magnetic field direction (B).
  • Middle finger = the direction of the Lorentz force (F).

For the second hand rule, use the open palm of the right hand and it is easier to use, especially if the angle is α≠90º, namely:

  • Thumb = direction of electric current (I).
  • The other four fingers = the direction of the magnetic field (B).
  • Palm = direction of Lorentz force (F).

It should be noted that the magnitude of the angle α does not affect the direction of the magnetic force. This is because the direction of the force is perpendicular to the direction of the electric current and magnetic field.

2. Lorentz Forces in Parallel Wires Carrying Electric Current

When there are two wires that have a length of I and then carry an electric current of I and the two wires are placed in a magnetic field of magnitude B, a magnetic force will occur. The electric force that occurs is both attractive and repulsive depending on the direction of the electric current coming from each wire.

When the two wires have the same current direction or the same direction, there will be an attractive force. Conversely, when the two wires have opposite current directions, a repulsive or opposing force will arise.

Regarding the magnitude of the attractive and opposing or repulsive forces on the two wires, you can use the formula:

Description:
1 = attractive or repulsive force on wire 1 (newtons).
2 = force of attraction or repulsion in wire 2 (newtons).
1 = strong current flowing at current 1 (amperes).
2 = strong current flowing at current 2 (amperes).
µ 0 = vacuum permeability.
I = wire length (meters).
α = distance between the two wires (meters).

3. Lorentz Force of Charge Moving in a Magnetic Field

When there is an electric charge q moving with speed v in a magnetic field B, a magnetic force will occur and it can be calculated by the formula:

Lorentz = qvB x sin α

Note:
q = electric charge (coloumb).
v = speed of movement (m/s).
B = magnetic field (tesla).
α = angle formed by B and v.

For the direction of the Lorentz force, this one is perpendicular to the direction in the magnetic field and the direction of the object’s velocity. The direction of this force will depend on the charge of the particle. Look at the picture below, according to the right-hand rule, if charge q has a positive value, then the direction of v will be parallel to I. Meanwhile, if charge q is negative, v will be opposite to I.

Then if the direction in the magnetic field is perpendicular to the direction of the velocity of the electrically charged particles, it causes a circular path, so that the particles will experience a centripetal force that is equal in magnitude to the magnetic force.

FLorentz = Fsentripetal

qvB = mv2 / R

That way, we can find the radius of the particle’s circular path using the formula:

R = mv/qvB

Factors Affecting the Lorentz Force

You need to know that there are several factors that affect the electric force, including:

  • Large electric current (I).
  • Magnetic field strength (B).
  • The length of the conveyor (I).

Application in Everyday Life

Information that is no less important is what are the benefits that we will get from applying the Lorentz force? One of the most pronounced benefits of applying this style is the electric motor. By flowing electricity into a coil in a magnetic field, a magnetic force can be generated in the form of the rotation of an electric motor used to drive the shaft, so that it can be used for various needs.

Apart from electric motors, we can also see the application of the Lorentz force in linear motors, railguns, electric generators, loudspeakers, linear alternatives, and many others.

Applications of the Lorentz force include the following:

  • Lorentz force velocimetry (LFV) is a non-contact electromagnetic flow measurement technique. Lorentz force velocimetry is well suited for velocity measurements of molten metals (such as steel or aluminum) and is currently being developed for metallurgical applications.
  • An electric motor is a device for converting electrical energy into mechanical energy. Electric motors are classified into two types, namely AC (alternating current) electric motors and DC (direct current) electric motors. Electric motors can be found in household appliances such as fans, washing machines, refrigerators, hair dryers and water pumps.
  • Pendorong magnetoplasmadynamic.
  • Electric generator.

Example Questions and Discussion

The Lorentz force is a force that arises due to the presence of an electric current (moving electric charge) in a magnetic field. For the direction of the Lorentz service, it is always perpendicular to the direction of the electric current (I) and the existing magnetic induction (B).

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Before heading to the example of the Lorentz force problem, you must go back to studying the following formulas.

Lorentz Force Formula of a Wire Moving in a Magnetic Field :

 

Information:

  • l = wire length (m).
  • I = strong current flowing in the wire (amperes).
  • B = magnetic field strength (tesla).
  • α = angle formed by B and I.

The Lorentz Force Formula for Electric Charges Moving in a Magnetic Field:

Information:

  • q = electric charge (coloumb).
  • v = speed of movement of electric charge (m/s).
  • B = magnetic field strength (tesla).
  • α = angle formed by B and v.

Lorentz force formula for two parallel current-carrying wires:

Information:

  • 1 = pull-attract or push-push force on wire 1 (newton).
  • 2 = pull-attract or push-push force in wire 2 (newton).
  • 1 = strong current flowing in wire 1 (amperes).
  • 2 = strong current flowing in wire 2 (amperes).
  • µ 0  is the vacuum permeability 
  • l = wire length (m).
  • α = distance between the two wires (m).

Example Question 1

Look at the following picture!

If an electric current I flows through wire AB, the direction of the magnetic force experienced by wire AB is…
A. to the
left B. to the
left C. to the right
D. perpendicular to the plane of the paper
E. perpendicular to the outside of the paper

Discussion:
Using the right hand rule, the current strength is indicated as the thumb, so the forefinger (magnetic field) will go out of the plane and based on the nature of the Lorentz force it will be perpendicular.

Answer: E. perpendicular to the surface of the paper.

Example Problem 2

A straight, current-carrying wire pointing east is placed in a magnetic field pointing north. In the conductor there will be a Lorentz force whose direction is ….
A. Northeast
B. Below
C. Up
D. West
E. South

Discussion:
To determine the direction of the Lorentz force we can use the right hand rule as follows.

Answer: D. West (perpendicular to B and I).

Example Problem 3

A wire with a length of 1 m has an electric current of 10 A. If the wire is placed in a 0.01 T magnetic field whose direction forms an angle of 30° to the direction of the current, the magnetic force experienced by the wire is … A. 0.05 N B.
0.5
N
C. 2 N
D. 4 N
E. 8 N

Discussion:
It is known:
L = 1 m
I = 10 AB
= 0.01 T
α = 30°

Dimensions: F = ?
Answer:
F = B . HE . L sin α
F = 0.01 T 10 A 1 m without 30°
F = 0.05 N

So, the magnetic force experienced by the wire is 0.05 N.

Example Problem 4

A straight wire with a current of 4 A is in a 1 T magnetic field that is perpendicular to the current. If the Lorentz force acting on the wire is 4 N, then the length of the wire is…

Discussion:
It is known:
L = 2 m
I = 20 AB
= 0.02 T
α = 30

Asked: F?
Answer:
F = BILsin30
F = 0.02.20.2.sin30
F = 0.4 N

So, the Lorentz force on the wire is 0.4 newtons.

Example Problem 5

An electron moving with a speed of 6000 m/s enters a magnetic field of 2000 T. If the direction of the velocity and the magnetic field forms an angle of 30 degrees, then the Lorentz force experienced by the electron is….

Discussion:
Given:
q = -1.6×10 -19  C (electron charge)
v = 6000 m/s
B = 2000 T
α = 30 degrees

Asked: F?
Answer:
F = qvBsin30
F = 1.6×10 -19 .6000.2000.1/2
F = 9.6 x 10 -13  N

So, the Lorentz force experienced by the electron is 9.6 x 10 -13  Newton.

 

Example Problem 7

A wire that is 500 cm long is in a magnetic field of strength 20 T. If the electric current flowing in the wire is 2 A, then what is the Lorentz force acting on the wire?

Discussion:
Known:
L = 500 cm = 0.5 m
B = 20 T
I = 2 A

Asked: How much Lorentz force does work on the wire?

Jawab:
F = BIL
= 20 T(2 A)(5 m)
= 200 N

The Lorentz force acting on the wire is 200 N.

Example Problem 8

A wire carrying an electric current of 20 A with an upward direction is in a magnetic field of 0.5 T by forming an angle of 30 o to the wire. If the length of the wire is 20 meters, how much Lorentz force will the wire experience?

 

 

Closing

Lorentz force materials are notoriously complicated materials, but they are actually quite easy to solve. The main concept is that you have to understand the direction of the variables that work, such as the direction of the electric current, the direction of the magnetic field and the direction of the Lorentz force itself.