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Lenz Law

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Last updated date: 18th Jul 2024
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What is Lenz’s Law?

Lenz’s Law named after the physicist Emil Lenz was formulated in 1834. It states that the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field.


When a current is induced by a magnetic field, then the magnetic field produced by the induced current will create its magnetic field. Thus, this magnetic field will be opposed by the magnetic field that created it. 


Lenz's law is based on Faraday's law of Induction which says, a changing magnetic field will induce a current in a conductor whereas Lenz's law tells us the direction of the induced current, which opposes the initial changing magnetic field which produced it. Hence, this is signified in the formula for Faraday's law by the negative sign.


\[ \epsilon = -\frac{d\Phi _{B}}{dt}\]


The magnetic field can be changed by changing its strength or by either moving the magnet towards or away from the coil, or moving the coil in or out of the magnetic field.


Hence we can say that the magnitude of the electromagnetic field induced in the circuit is proportional to the rate of change of flux.


\[ \epsilon \alpha  \frac{d\Phi _{B}}{dt}\]


Lenz Law Formula:

According to Lenz's law, when an electromagnetic field is generated by a change in magnetic flux, the polarity of the induced electromagnetic field produces an induced current whose magnetic field opposes the initial changing magnetic field which produced it.


The formula for Lenz law is shown below:

\[ \epsilon = -N(\frac{d\Phi _{B}}{dt})\]

Where,

\[ \epsilon \] = induced EMF

\[d\Phi _{B}\]  =  change in magnetic flux

N = number of turns in the coil


Lenz law applications:

The Applications of Lenz's Law Include:

When a source of an electromagnetic field is connected across an inductor, a current starts flowing through it. The back electromagnetic field will oppose this increase in current through the inductor. To establish the flow of current, the external source of the electromagnetic field has to do some work for overcoming this opposition.

  1. Lenz’s law is used in electromagnetic brakes and induction cooktops.

  2. It is also applied to electric generators, AC generators.

  3. Eddy Current Balances

  4. Metal detectors

  5. Eddy current dynamometers

  6. Braking systems on train

  7. Card Readers

  8. Microphones


Lenz Law Experiment:

To find the direction of the induced electromotive force and current we use Lenz’s law. Some experiments are below.


First Experiment:

In the first experiment, when the current in the coil flows in the circuit, the magnetic field lines are produced. As the current flows through the coil increases, the magnetic flux will increase. The direction of the flow of induced current would be such that it opposes when the magnetic flux increases.


Second Experiment:

In the second experiment, when the current-carrying coil is wound on an iron rod with its left end behaving as N-pole and is moved towards the coil S, an induced current will be produced.


Third Experiment:

In the third experiment, the coil is pulled towards the magnetic flux, the coil linked it goes on decreasing which means that the area of the coil inside the magnetic field decreases. 


According to Lenz’s law, the motion of the coil is opposed when the induced current is applied in the same direction.


To produce current, force is exerted by the magnet in the loop. To oppose the change a force must be exerted by the current on the magnet.


An example of Lenz Law:

In a copper or aluminum pipe, there is the presence of large magnetic fields that cause counter-rotating currents. Dropping the magnet through the pipe demonstrates this particular phenomenon. When the magnet is being dropped within the pipe it tends to descend at a rate that is lower than when it is dropped outside the pipe. Here there is a current induced which can be determined using the right-hand rule.

FAQs on Lenz Law

1. How does Lenz’s law relate to the conservation of energy?

Lenz’s law is based on the law of conservation of energy. From the definition of Lenz’s law, it is seen that the current will always flow in the opposite direction of the object or the cause that has produced it. Therefore there is more work that needs to be done to go against an opposing force. This work done against the opposing force hence results in a change in the magnetic flux because of which the current is induced. The extra work that is done is converted to electrical energy which is the law of conservation of energy.

2. What is the history of Lenz law?

Heinrich Lenz is also referred to as Emil Lenz. He was a Baltic German physicist who may not have reached his fame in the early 1900s unlike his peers Michael Faraday who was known to solve a lot of mysteries related to electromagnetism. The law received the name Lenz for the fast and comprehensive documentation that the experiments had along with the dedication to the scientific method which was not common at that time. This law also forms an important part of Faraday’s laws and hence tells about the direction in which the current tends to flow.

3. How do Lenz law and Faraday's law relate to each other?

Lenz law is encapsulated in Faraday’s laws as it tells us why the direction in which the induced current tends to flow. The easiest way to state the Lenz law is that the change in magnetic flux tends to induce a current which is in a direction that is opposite to the object that has generated it. It can hence also be said that when the current flows, it creates its own magnetic field. The direction of the current will be such that the new magnetic field is in the opposed direction of the flux changes that have created it. This law is part of the Lenz law as it consists of a negative sign that indicates the EMF opposes the original change in magnetic flux.

4. What are eddy currents and how are they understood by using Lenz law?

Eddy’s current is a small electric current that follows Lenz law. While it is used to refer to small currents it actually generates a large looping current in conductors. When a conductor is moved through the magnetic field there is a production of electric currents being generated which is in line with Lenz’s law and counteracts the effect of motion leading to magnetic damping. This sort of motion where the field that is induced works against the motion through which it is created tends to be heavily used in magnetic braking systems such as roller coasters.

5. Why should students learn Lenz’s law?

Lenz’s law has a variety of applications and is quite important in the history of currents. This law that tells students a lot regarding the concepts that are used in various machines helps students to learn about these machines and how they work. With the help of this law, there is basic knowledge regarding how the conservation of energy takes place while there is opposed motion being observed.