Lenz’s Law
Lenz's Law is a fundamental principle in electromagnetism that describes how induced currents behave in response to changes in magnetic fields. It states that the direction of the induced current in a closed loop is such that it creates a magnetic field that opposes the change in the original magnetic field. This principle is rooted in the conservation of energy, ensuring that energy cannot be created or destroyed, thus preventing the possibility of an infinite current or energy in a closed system.
The application of Lenz's Law is seen in various technologies, such as inductive loop sensors used in traffic lights, which detect the presence of vehicles based on changes in magnetic fields caused by the metal in cars. The law also underpins the operation of generators, where mechanical energy (from sources like water, steam, or wind) is converted into electrical energy by the movement of magnets relative to coils of wire.
To determine the direction of induced currents, the right-hand rule is often employed, allowing users to visualize the relationship between current and magnetic field direction. Overall, Lenz's Law plays a critical role in understanding and harnessing electromagnetic phenomena in everyday applications and advanced technologies.
Lenz’s Law
FIELDS OF STUDY: Classical Mechanics; Electromagnetism; Electronics
ABSTRACT: Coils react to any change in the magnetic environment around them. Induced currents are created in the coils to work against any change in magnetic field. Lenz’s law states that in order to conserve energy, the induced current in a loop produces a magnetic field, which then opposes any changes in the existing magnetic field through the loop. By using coils and changing magnetic fields, humans have been producing electricity for decades.
Principal Terms
- conservation of energy: total amount of energy in a closed system is always the same, therefore energy can neither be created nor destroyed.
- current: the motion of charged particles as a function of time.
- electromagnetic field: a field created by the motion of charged particles.
- Faraday’s law: a physical law that explains how changes in the strength of magnetic fields through coils induce a current in the coil to counteract the change in the magnetic field.
- inductance: the property by which a current is created in conductors to resist a change in the magnetic field through the conductor.
- right-hand rule: a technique used to find the direction of magnetic forces and induced currents by using the right hand. The direction of the current is expressed by the fingers, and the direction of the magnetic field is expressed by the extended thumb.
Induced Currents
Michael Faraday (1791–1867) was a British scientist who experimented extensively with currents. Although he had no formal training in physics, he was able to discover an important relation between electricity and magnetism. Faraday found that currents are induced by changing magnetic fields and currents create magnetic fields. The motion of charged particles creates electromagnetic fields. The two physical concepts are related. This is the basis of electric generators. By spinning coils around magnets or magnets around coils, electricity can be produced. Because Faraday did not have any formal training, he could not explain these effects with mathematics. It took many years and the work of Scottish physicist James C. Maxwell (1831–79) to discover the mathematical law that explains Faraday’s discoveries. In order to correctly predict the behavior of induced currents, Maxwell had to include Lenz’s law. The law states that the induced current in a loop produces a magnetic field, which then opposes any changes in the existing magnetic field through the loop.
The Magnetic Field of a Car
When a motor vehicle stops at a traffic signal, a sensor is activated in order to detect the waiting vehicle. Many people assume that a pressure sensor is used, but if that were the case, smaller vehicles such as motorcycles would have a hard time activating the sensor. Instead, an inductive loop sensor is used, and it is designed to detect changes in the magnetic field.
Cars and other motor vehicles are made of parts that contain ferromagnetic materials, which create magnetic fields. When a car stops at a red light, the magnetic field produced by the car induces a current in an inductive loop sensor. The size of the current created is relative to the magnetic field’s strength and the inductance of the coil. This, in part, is analyzed by the electronics near the traffic light, which then trigger the light to change. These inductive loop sensors work on two basic laws of electromagnetism: Faraday’s law and Lenz’s law.
Faraday’s law states that changes in the strength of magnetic fields through coils induce a current in the coil to counteract the change in the magnetic field. An inductive loop sensor is basically a loop of wire. The voltage induced (Vind) in the inductive loop or any other coil of wire is equal to the magnetic flux (∆Φ) divided by the amount of time it takes for the field to change (t), expressed as
The magnetic flux is a function of the magnetic field strength (B), the cross-sectional area of the loop exposed to the magnetic field (A), the number of turns in the loop (N), and the amount of time it takes for the field to change (t), or
In the example above, the area of the loop permeated by the magnetic field is constant. Therefore, the equation can be simplified to
In order to find the current through the loop, one must apply Ohm’s law in combination with Faraday’s law. Ohm’s law states that the voltage (V) is the product of the current (I) and the resistance (R), or
V = IR
By substituting this into Faraday’s law, the induced current in the inductive loop sensor can be obtained. Mathematically this is expressed as
Lenz’s law explains why a negative sign precedes the equation in Faraday’s law. If the negative sign were not included, it would mean the induced current could create a magnetic field that enhances the existing magnetic field through the coil. In turn, this magnetic field would produce more current that would then produce even more magnetic field. The system would produce a feedback that would take the current into infinity. The law of conservation of energy states that in a closed system, the total amount of energy is always the same; energy in a closed system can neither be created nor destroyed. If an infinite current is induced, the implication is an infinite amount of energy, which is impossible. The negative sign in Faraday’s law carries this second important property. It balances the magnetic field and makes the system conserve energy by keeping the induced currents opposing any change.
In order to correctly find the directions of the induced currents, a simple technique was devised. This technique, known as the right-hand rule, uses an individual’s right hand. First, point the fingers of the right hand in the direction of the current. If it is a coil, curl the fingers so that they are pointing in the direction of the current. Next, extend the thumb, which will then be pointing in the direction of the induced magnetic field. This technique is also effective if the thumb of the right hand is first pointed in the direction of the induced magnetic field, with the fingers then naturally curling in the direction of the induced current.
Sample Problem
A coil of copper wire is being used by high school physics students in order to energize a light bulb. The students bring the north pole of a bar magnet closer to the coil of wire from the left side of the coil. What is the direction of the induced current in the coil?
Answer:
Iind is counterclockwise.
Using Lenz’s law, it is understood that a coil’s induced current opposes any change in the magnetic environment around it. By bringing a magnet’s north pole closer to the coil and from the left, the magnetic field is increasing in strength. Therefore, there are more magnetic field lines going through the coil to the right. The coil opposes this extra field, so it produces a field that is to the left. To find the direction of the current that produces the magnetic field, use the right-hand rule. Place the thumb of the right hand in the direction of the magnetic field, left. Now curl the fingers, and the direction of the fingers is the direction of the induced current, which in this case is counterclockwise.
Generating Electricity
Alternating current (AC) is produced by generators at power plants that use the principles described by Faraday’s and Lenz’s laws. These generators, whether powered by falling water, steam, or wind, consist of coils of wire and magnets. As the water, steam, or wind makes a turbine spin, the main shaft, which has magnets attached to it, also turns. When a magnet crosses in front of one of the coils, it increases the magnetic field through the coil. This induces a current in the coil, which creates a magnetic field to cancel the extra magnetic field through the coil. As the turbine keeps spinning, the magnet moves away from the coil. Then, the coil has less magnetic field through it, and an induced current is created on the coil to increase the magnetic field through the coil. In other words, coils resist change and fight against any change in the magnetic field through them. If enough time passes, the coil gets used to the change and the induced currents disappear. But by that time, the shaft has spun more, and another magnet has moved in front of the coil.
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