Gavin Howe
Faraday's law of induction, Ampere's circuital law, Lenz's law, and the Lorentz force law are the fundamental laws that govern the operation of electric motors. Faraday's law of induction, discovered by Michael Faraday in 1831, states that a change in the magnetic environment of a closed coil of wire induces a voltage or electromotive force (EMF) in the coil. The Lorentz force law, on the other hand, describes the force experienced by a charged particle moving in a magnetic and electric field, given by the equation F = q(E + v x B). While Faraday's law focuses on the relationship between induced EMF and the rate of change of magnetic flux, the Lorentz force law predicts the direction of the current using the right-hand rule.
| Characteristics | Values |
|---|---|
| Definition | Lorentz force: A magnetic force that acts on a charged particle that is moving through a magnetic field. |
| Faraday's law: A law that states that a change in magnetic flux induces an electromotive force (EMF) and, subsequently, a current in a closed conducting loop. | |
| Discovery | Lorentz force: Discovered by either James Clerk Maxwell or Oliver Heaviside. Credit is typically given to Heaviside. |
| Faraday's law: Discovered by Michael Faraday in 1831. It was later described mathematically and incorporated into a broader electromagnetic theory by James Clerk Maxwell in the 1860s. | |
| Application | Lorentz force: Used to predict the direction of current in a wire moving through a magnetic field. |
| Faraday's law: Used to explain the operation of electric motors and the generation of electromotive force (EMF) and current. | |
| Equations | Lorentz force: The Lorentz force equation is given by F = q(E + v x B) where F is the force, q is the charge, E is the electric field, v is the velocity, and B is the magnetic field. |
| Faraday's law: Faraday's law can be expressed as EMF = - dΦ/dt, where EMF is the electromotive force and dΦ/dt represents the rate of change of magnetic flux over time. | |
| Rules | Lorentz force: The direction of the Lorentz force can be determined using the right-hand rule, where the thumb points in the direction of the current, and the middle finger points in the direction of the force. |
| Faraday's law: Fleming's left-hand rule is applicable in certain scenarios involving wires cutting through magnetic field lines. |
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What You'll Learn
Faraday's Law and Lorentz Force are both fundamental to electromagnetism
Faraday's Law and the Lorentz Force are both fundamental to electromagnetism. Faraday's Law of induction is the fundamental law on which electric motors operate. It describes how a time-varying magnetic field induces an electric field, which drives a current around a loop. This is represented by the Maxwell-Faraday equation.
The Lorentz Force, on the other hand, is the force experienced by a particle due to electric and magnetic fields. An electric field will exert a force on a particle whether it is moving or stationary, whereas a magnetic field will only exert a force on a particle when it is in motion. The direction of the Lorentz Force can be determined using the right-hand rule, where the thumb points in the direction of the current, and the first finger points in the direction of the magnetic field. The second finger then points in the direction of the force.
The two laws are closely related. The Lorentz Force Law can be used in conjunction with the Maxwell-Faraday equation to correctly calculate the electromotive force. The Lorentz Force Law also predicts an EMF in certain situations where Faraday's Law does not, such as with a magnet rotating in front of a metal disk.
In summary, Faraday's Law and the Lorentz Force Law are both essential in understanding electromagnetism and the behaviour of electric motors. They are complementary, with the Lorentz Force Law providing additional information and predictions that Faraday's Law alone cannot.
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Faraday's Law describes a wire cutting through a magnetic field
Faraday's Law, also known as Faraday's Law of Induction, describes the fundamental operating principle of transformers, inductors, and many types of electric motors, generators, and solenoids.
Faraday's Law can be observed in action through experiments. For example, when a bar magnet is rapidly moved into or out of a coil of wire, transient currents are induced. Another experiment involves holding a magnet stationary and moving a coil of wire back and forth within the magnetic field, which induces an electric current in the coil.
The Lorentz Force, on the other hand, is the force that a particle experiences due to electric and magnetic fields. Electric fields exert a force on a particle whether it is moving or not, whereas magnetic fields only exert a force when the particle is in motion. The Lorentz Force law predicts an EMF, while Faraday's Law does not. The direction of the Lorentz Force can be determined using the right-hand rule, where the thumb points in the direction of the current, and the middle finger points in the direction of the force.
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Lorentz Force predicts EMF in certain scenarios
Lorentz Force law can be used to predict the direction of current and, thus, predict EMF in certain scenarios. The direction of the Lorentz force is derived using the right-hand rule: point your thumb in the direction of the current, your first finger in the direction of the magnetic field, and your second finger will point in the direction of the force.
In the case of a conducting rod moving through a magnetic field, the Lorentz force drives the mobile electrons of the conductor along the length of the rod, leading to a separation of charge between the two ends of the rod. This is the basic mechanism behind motional EMF.
In the case of a wire extended between the tips of a plane's wings flying through a magnetic field, there is no change in magnetic flux density, so no change in flux linkage and ultimately no induced current. However, as the plane is accelerating, it cuts the field lines at a greater rate, so according to Faraday's law, a voltage will be induced.
In the case of a disc rotating with angular rate ω in a static magnetic field, the magnetic Lorentz force v × B drives a current along the conducting radius to the conducting rim, generating an EMF. This is an example of a scenario where no flux is changing, but an EMF is induced by the Lorentz force.
In summary, the Lorentz force law can be used to predict EMF in certain scenarios, such as when a conducting rod is moving through a magnetic field, when a wire is extended between the tips of a plane's wings flying through a magnetic field, or when a disc is rotating in a static magnetic field.
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Faraday's Law of Induction is the basis for electric motors
Faraday's law of induction, also known as the flux rule, states that the electromotive force (EMF) around a closed circuit is equal to the negative rate of change of the magnetic flux through the circuit. In other words, the faster the magnetic field changes, the greater the voltage in the circuit will be. The direction of the change in the magnetic field determines the direction of the current.
Faraday's law of induction is the fundamental law on which electric motors operate. It describes how an electric current produces a magnetic field and, conversely, how a changing magnetic field generates an electric current. This is known as electromagnetic induction, which is the basic principle of operation of transformers, motors, and generators.
Michael Faraday discovered electromagnetic induction in the 1830s. He observed that when a permanent magnet was moved in and out of a coil or a single loop of wire, it induced an EMF, or voltage, and thus produced a current. Faraday's law was later incorporated into the more comprehensive Maxwell's equations, which were developed by Scottish physicist James Clerk Maxwell to explain the relationship between electricity and magnetism.
The Lorentz force, on the other hand, is the force that a particle experiences due to electric and magnetic fields. Electric fields exert a force on a particle whether it is moving or not, while magnetic fields exert a force only when the particle is in motion. The direction of the Lorentz force is derived using the right-hand rule, where the thumb points in the direction of the current, the first finger points in the direction of the magnetic field, and the second finger points in the direction of the force.
While Faraday's law and the Lorentz force are distinct concepts, they are both fundamental to the understanding of electromagnetism and the operation of electric motors.
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The Lorentz Force is derived using the right-hand rule
The Lorentz force is defined as the combination of the magnetic and electric force on a point charge due to electromagnetic fields. It was derived by Hendrik Lorentz in 1895. The Lorentz force is used in electromagnetism and is also known as the electromagnetic force.
The Lorentz force law/right-hand rule can be used to predict the direction of current. The right-hand rule is a convention and a mnemonic used to define the orientation of axes in three-dimensional space. It is also used to determine the direction of the cross product of two vectors and to establish the direction of the force on a current-carrying conductor in a magnetic field. The right-hand rule was introduced in the 19th century by John Fleming in his book 'Magnets and Electric Currents'.
The direction of the Lorentz force is derived using the right-hand rule. To determine the direction of the magnetic force on a positive moving charge, point your right thumb in the direction of the velocity (v), your index finger in the direction of the magnetic field (B), and your middle finger will point in the direction of the resulting magnetic force (F). Negative charges will be affected by a force in the opposite direction.
The right-hand rule is useful to find the magnetic force as it becomes easy to visualize the direction as given in Lorentz's force law. The right-hand rule is also known as Ampère's right-hand grip rule, the right-hand screw rule, the coffee-mug rule, or the corkscrew rule.
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Frequently asked questions
Faraday's law of induction explains electromagnetic induction, which is the process of generating an electric current by changing the magnetic field around a conductor. Faraday's law dictates proportionality between an induced EMF and the rate of change of flux linkage.
The Lorentz force is the force experienced by a charged particle moving in a magnetic and electric field. The direction of the Lorentz force is derived using the right-hand rule.
Faraday's law can be used in any situation where the magnetic flux is changing through a closed conducting loop. The Lorentz force law, on the other hand, gives the motional EMF. The two can be combined to give the net EMF.
