In physics, the Lorentz force is the pair of electric force and magnetic force on a charged point particle caused by electromagnetic fields. In other words, the Lorentz force is the force applied to a charged particle with a velocity along an electric field and magnetic field.
Lorentz Force
The total electromagnetic force on a given particle is known as the Lorentz force. It is named after the physicist Hendrik A. Lorentz.
The Lorentz force is given by,
F = qE + qv × B
Where,
F is the Lorentz force
q is the charge of the given particle
E is the electric field
B is the magnetic field
v is the velocity
The magnetic force is proportional to the value of the vector cross product v × B and q. In the case of the angle Ï• between B and v, the value of the force is equivalent to qvB sin Ï•. In a uniform magnetic field, the Lorentz force causes the motion of charged particles. If velocity v is perpendicular to magnetic field B, the charged particle will move in a circular path with a radius (r) equal to mv/qB. If the angle Ï• is zero, then there is no magnetic force on the charged particle (it will continue to travel undeflected through the field lines).
Particle accelerators like cyclotrons exploit the fact that the charged particles travel in circular orbits when B and v are perpendicular to each other. For every revolution, a precisely driven electric field imparts the charged particles with extra kinetic energy. This allows them to move in larger orbits. When these particles have the ideal energy, they are utilised in a number of various ways. It is applied in the study of subatomic particles to various medical treatments.
Lorentz Force Key Points
Maxwell’s equations show how electrically charged particles and moving charged particles or currents generate magnetic and electric fields. On the other hand, the Lorentz force law extensively concluded the overall picture by showing the force exerting on a moving charge q in an electromagnetic field. The Lorentz force describes the impact of B and E on a point electric charge. However, such EM forces do not give the whole picture. Electrically charged particles are most probably coupled to other forces like nuclear force and gravity. So, the equations of Maxwell do exist independent from other physical laws but are connected to them through the current densities and charge. The effect of a charged particle on the Lorentz force is one aspect. The creation of B and E by charges and currents is the other aspect. In real substances, the Lorentz force is not enough to explain the overall behaviour of the point particles, both as computation and in principle. In material mediums, these particles not only react to the B and E fields but also produce these fields. Complicated equations must be answered to find the spatial response and the time of charges. For example, analyse fluid dynamics, electrohydrodynamics, magnetohydrodynamics, and superconductivity.
The video describes the fundamentals of magnetic field and magnetic field lines
Magnetic Field and Magnetic Field Lines: What is a Magnetic Field?
Applications of Lorentz Force
The important applications of Lorentz force are given below.
Particle accelerators like cyclotrons utilise the Lorentz force. A bubble chamber makes use of the Lorentz force to create the graph for obtaining the paths of charged particles. Cathode ray televisions employ the concept of Lorentz force to drive the electrons in a straight line so as to land on particular points on the screen.
The Lorentz force exists in numerous electric devices such as particle accelerators, mass spectrometers, magnetrons, velocity filters, and Lorentz force calorimetry.
In its manifestation as the Laplace force on a current in a conductor, this force occurs in many electrical devices, including electric motors, railguns, linear motors, loudspeakers, magnetoplasmadynamic thrusters, loudspeakers, homopolar generators, electrical generators, and linear alternators.
Important Lorentz Force Questions with Answers
1) What is the Lorentz force?
The Lorentz force is the pair of electric force and magnetic force on a charged point particle caused by electromagnetic fields. In other words, the Lorentz force is the force applied to a charged particle with a velocity along an electric field and magnetic field.
2) What is the formula to calculate the Lorentz force?
The total electromagnetic force on a given particle is known as the Lorentz force. It is named after the physicist Hendrik A. Lorentz.
The Lorentz force is given by,
F = qE + qv × B
Where,
F is the Lorentz force
q is the charge of the given particle
E is the electric field
B is the magnetic field
v is the velocity
3) How do particle accelerators utilise the Lorentz force?
Particle accelerators like cyclotrons exploit the fact that the charged particles travel in circular orbits when B and v are perpendicular to each other. For every revolution, a precisely driven electric field imparts the charged particles with extra kinetic energy. This allows them to move in larger orbits. When these particles have the ideal energy, they are utilised in a number of various ways. It is applied in the study of subatomic particles to various medical treatments.
4) The Lorentz force is named after the physicist _____.
Answer: Hendrik Lorentz
Explanation: The Lorentz force is named after the physicist Hendrik Lorentz.
5) How many Gauss is equal to one Tesla?
One Tesla is equal to 10,000 Gauss.
6) Which are the familiar devices that use the Lorentz force?
Cyclotrons and other circular path particle accelerators, mass spectrometers, velocity filters, magnetrons and Lorentz force velocimetry use the Lorentz force.
In its manifestation as the Laplace force on a current in a conductor, this force occurs in many electrical devices, including electric motors, railguns, linear motors, loudspeakers, magnetoplasmadynamic thrusters, loudspeakers, homopolar generators, electrical generators, and linear alternators.
7) What is the role of the Lorentz force in cathode ray televisions?
Cathode ray televisions employ the concept of Lorentz force to drive the electrons in a straight line so as to land them on particular points on the screen.
8) What is the main drawback of the concept of the Lorentz force?
The Lorentz force describes the impact of B and E on a point electric charge. However, such EM forces do not give the whole picture. Electrically charged particles are most probably coupled to other forces like nuclear force and gravity. So, the equations of Maxwell do exist independent from other physical laws but are connected to them through the current densities and charge. In real substances, the Lorentz force is not enough to explain the overall behaviour of the point particles, both as computation and in principle. In material mediums, these particles not only react to the B and E fields but also produce these fields.
9) ______ is proportional to the value of the vector cross product v × B and q.
Answer: The magnetic force
Explanation: The magnetic force is proportional to the value of the vector cross product v × B and q.
10) ______ show how electrically charged particles and moving charged particles or currents generate magnetic and electric fields.
Answer: Maxwell’s equations
Explanation: Maxwell’s equations show how electrically charged particles and moving charged particles or currents generate magnetic and electric fields.
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Practice Questions
1) Define the Lorentz force law.
2) What are the main Maxwell’s equations?
3) What is the Lorentz force equation?
4) What is the significance of the Lorentz force?
5) How do the bubble chambers use Lorentz force?
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