Question

State Lenz’s law and explain that it follows the law of conservation of energy.

Hint:

To easily find the current direction based on Lenz's law: - Looking at a coil face, if it acts like a North Pole to repel an approaching N-pole, the current must flow in an Anti-Clockwise direction. - If it acts like a South Pole to pull back a receding N-pole, the current flows in a Clockwise direction. Remember: "Nature abhors a change in magnetic flux!"

Answer 1

Concept: Lenz's Law provides a physical method for determining the direction of an induced electromotive force (emf) or induced electrical current resulting from electromagnetic induction. It is a fundamental law embedded within Faraday's mathematical law of induction, represented explicitly by the negative sign in the expression: \[ \varepsilon = - \frac{d\Phi_B}{dt} \] Where \(\varepsilon\) is the induced electromotive force and \(\frac{d\Phi_B}{dt}\) is the time rate of change of magnetic flux linked through the circuit loop area. Statement of Lenz’s Law:
Lenz's Law states that: "The direction of the induced current or induced electromotive force in a closed circuit is always such that it opposes the change in magnetic flux that produced it." Detailed Explanation of Conservation of Energy via Lenz's Law:
To understand how Lenz's law is a direct consequence of the universal law of conservation of energy, let us perform a detailed thought experiment using a bar magnet and a closed conducting loop.
• Moving the North Pole towards the Coil:
• Consider a closed circular conducting wire loop. Let the North Pole ($N$) of a permanent bar magnet be moved continuously towards one of the open faces of this coil.
• As the magnet approaches, the magnetic flux passing through the cross-sectional area of the coil increases over time.
• According to Lenz's law, an induced current will be established in the coil to oppose this increasing magnetic flux. To counteract the approaching North Pole, the face of the coil facing the magnet must develop a local North polarity.
• Like magnetic poles naturally repel each other. Therefore, a repulsive magnetic force acts between the approaching magnet and the coil face.
• To continue moving the magnet closer to the loop, an external agent must perform mechanical work against this repulsive force.
• Moving the North Pole away from the Coil:
• Conversely, if we attempt to withdraw the North Pole ($N$) of the bar magnet away from the loop, the magnetic flux linked with the coil decreases over time.
• To oppose this decrease, Lenz’s law dictates that the coil will set up a current that attempts to attract and retain the receding magnet. Therefore, the face of the coil will establish a local South polarity.
• Unlike poles naturally attract each other. As a result, an attractive magnetic force pulls back against the moving magnet.
• To continue pulling the magnet away from the coil, the external agent must again perform mechanical work, this time against the attractive force.
• Energy Conversion Mechanism:
• In both scenarios, mechanical energy is expended by the external agent to overcome the opposing forces created by the induced currents.
• This expended mechanical work is transformed into electrical energy within the wire loop, which manifests as an induced current. This electrical energy eventually dissipates as heat energy via Joule heating (\(I^2Rt\)) due to the internal resistance of the wire.
• What if Lenz's Law were False? (Proof by Contradiction):
• Imagine that Lenz's law did not hold, and instead, the induced current helped or accelerated the change in magnetic flux.
• If you pushed a North Pole toward a coil, the coil face would develop a South Pole to attract it.
• The magnet would be pulled inward automatically, accelerating on its own without any external mechanical work. As its velocity increased, the rate of change of flux would increase, generating even more current and greater kinetic energy simultaneously. This scenario implies creating electrical and kinetic energy out of absolutely nothing!
• This violates the First Law of Thermodynamics (Conservation of Energy), proving that the induced current must oppose the change in flux. Thus, Lenz's law is a necessary manifestation of the law of conservation of energy.