Lenz’s Law:
Lenz’s Law states that the direction of the induced current in a circuit is such that the magnetic field produced by it opposes the change in magnetic flux that produces it. In simple words, the induced current always acts in a direction to oppose the cause that produces it.
Mathematically, it is expressed as:
E = − dΦ/dt
The negative sign indicates the opposition described by Lenz’s Law.
Showing that Lenz’s Law is a Consequence of the Law of Conservation of Energy:
Step 1: Consider a Magnet Approaching a Coil
Suppose a bar magnet is moved towards a closed conducting coil. As the magnet approaches, the magnetic flux linked with the coil increases. According to Faraday’s Law, an induced current is produced in the coil.
Step 2: Direction of Induced Current
According to Lenz’s Law, the induced current flows in such a direction that it produces a magnetic field which opposes the approaching magnet. This means the face of the coil near the magnet behaves like a similar magnetic pole, creating a repulsive force.
Step 3: Relation with Conservation of Energy
Because of this opposition, an external force must be applied to keep moving the magnet towards the coil. Work has to be done against the repulsive force. This mechanical work done by the external agent is converted into electrical energy in the circuit (in the form of induced current and heat).
If the induced current were to assist the motion of the magnet instead of opposing it, the magnet would accelerate without any external work being done. This would result in the continuous production of electrical energy without energy input, which would violate the Law of Conservation of Energy.
Conclusion:
Thus, Lenz’s Law ensures that energy is conserved. The induced current always opposes the change in magnetic flux so that mechanical energy supplied from outside is converted into electrical energy. Therefore, Lenz’s Law is a direct consequence of the Law of Conservation of Energy.