1. Concept Overview
Lenz’s law helps me find the direction of the induced current when magnetic flux changes. While Faraday’s laws tell me that an emf is induced, Lenz’s law tells me how the induced current flows in response.
The main idea is simple: the induced current always flows in such a way that it opposes the change in magnetic flux that produced it. Nature always resists sudden changes, and this law is a perfect example of that idea.
1.1. One-line idea I remember
Induced current opposes the cause producing it.
2. Statement of Lenz’s Law
Lenz’s law states:
The direction of the induced current is such that its magnetic effect opposes the change in magnetic flux that caused it.
This is why Faraday’s law has a negative sign:
\( \varepsilon = -\dfrac{d\Phi_B}{dt} \)
The negative sign reminds me that the induced emf fights against the flux change.
2.1. Meaning of “opposes the change”
Opposition does not mean stopping the change completely. It only means resisting it. The induced current tries to create a magnetic field that either pushes back against an increase in flux or tries to fill in when flux is decreasing.
3. Why Opposition is Necessary
I always remind myself that Lenz’s law is basically a reflection of energy conservation. If the induced current helped the change instead of opposing it, we could get unlimited energy from nowhere, which is impossible.
Opposition ensures that work must be done to change flux, and this work becomes electrical energy.
3.1. Example of energy reasoning
If a magnet is pushed quickly into a coil, I feel a resisting force. This resistance is because the coil produces an induced magnetic field that pushes back. The work I do against this resistance becomes the induced electrical energy in the coil.
4. Understanding Lenz’s Law With Magnet and Coil
To understand the law better, I imagine a bar magnet moving towards or away from a coil connected to a galvanometer.
4.1. Case 1: Magnet approaching the coil
When the north pole approaches the coil, the magnetic flux through the coil increases. According to Lenz’s law, the induced current must oppose this increase. So the coil tries to create its own north pole facing the incoming magnet. This creates a repulsive effect.
4.2. Case 2: Magnet moving away from the coil
As the magnet moves away, flux decreases. Now the coil tries to oppose the reduction by creating a south pole facing the retreating magnet. This creates an attractive effect.
4.3. Key point
Whether the magnet is approaching or moving away, the coil responds in such a way that the induced current resists the change in flux in every situation.
5. Direction of Induced Current Using Lenz’s Law
Lenz’s law gives a conceptual method to find the direction of current. I identify whether the flux is increasing or decreasing, then think: what magnetic field should the coil produce to oppose that change?
5.1. How I apply it step by step
- Find whether magnetic flux is increasing or decreasing.
- Decide what magnetic field the coil needs to create to oppose that change.
- Use the coil’s polarity to determine the direction of current (clockwise or anticlockwise).
This method works even without using the right-hand rule.
5.2. Using polarity of the coil
If the coil must create a north pole towards the magnet, the induced current will flow in a direction that creates that pole. Similarly, if it must create a south pole, the current direction reverses.
6. Lenz’s Law and Faraday’s Law
Lenz’s law and Faraday’s law work together. Faraday’s law tells me the magnitude of the induced emf. Lenz’s law tells me the direction of the emf. This combination gives the complete picture of electromagnetic induction.
6.1. Connecting the two laws
The negative sign in Faraday’s law comes directly from Lenz’s law:
\( \varepsilon = -\dfrac{d\Phi_B}{dt} \)
This negative sign ensures that the induced current always follows Lenz’s direction rule.
7. Examples That Show Lenz’s Law Clearly
There are many simple situations where the law can be seen in action. These examples help fix the idea in my mind.
7.1. Falling magnet through a copper tube
A magnet falls slowly through a thick copper tube compared to normal free fall. As the magnet falls, the changing flux induces currents in the tube that create magnetic fields opposing the fall. This slows the magnet down.
7.2. Sliding a conductor on a U-shaped track
When the conductor slides in a magnetic field, the flux changes. The induced current creates a magnetic force that resists the motion, making the rod feel harder to move.
7.3. Approaching and withdrawing magnets
In both situations, the coil generates a magnetic field that opposes the change — repelling when the flux increases and attracting when the flux decreases.