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Lenz's law Knowledge-Based Study

Physics · Magnetism & Electromagnetism · Physics · Electromagnetic Induction

Physics topic explanations on Lenz's law.

Study notes

  1. What is Lenz's Law?

    Lenz's law provides the direction of an induced electromotive force (emf) and induced current resulting from electromagnetic induction. Formulated by Heinrich Lenz in 1834, the law states:

    The direction of an induced current is always such that its magnetic field opposes the change in magnetic flux that produces it.

    In mathematical terms, Faraday's law of induction is expressed as:

    ε = -dΦB / dt

    The negative sign in this equation directly represents Lenz's law, showing that the induced electromotive force (ε) acts in opposition to the rate of change of magnetic flux (dΦB / dt).

    How Opposition Operates

    It is essential to recognize that the induced current does not necessarily oppose the external magnetic field itself; rather, it opposes the change in the external magnetic flux through the circuit.

    • Increasing Flux: When the magnetic flux through a conducting loop is increasing, the induced magnetic field points in the opposite direction to the external field to resist the increase.
    • Decreasing Flux: When the magnetic flux through a conducting loop is decreasing, the induced magnetic field points in the same direction as the external field to sustain the falling flux.

    Once the required direction of the induced magnetic field is determined, the right-hand grip rule is applied to determine the direction of the induced current: curl the fingers of your right hand around the loop in the direction of the current, and your thumb points in the direction of the induced magnetic field.

    Lenz's Law and the Conservation of Energy

    Lenz's law is a direct consequence of the principle of conservation of energy.

    Consider pushing the north pole of a bar magnet toward a closed conducting loop:

    • According to Lenz's law, the induced current produces a magnetic field with its north pole facing the approaching magnet, creating a repulsive magnetic force.
    • To move the magnet closer, external mechanical work must be done against this repulsive force.
    • This mechanical work is converted directly into electrical energy, which then dissipates as thermal energy due to the resistance of the loop.

    If the opposite were true and the induced field attracted the approaching magnet, the magnet would accelerate without any external input of work, generating electrical energy from nothing and violating the law of conservation of energy.

    Applications of Lenz's Law

    The opposition described by Lenz's law has several practical consequences and engineering applications:

    • Eddy Current Braking: Smooth, non-contact braking systems used in high-speed trains and roller coasters rely on eddy currents induced in metal wheels or rails. The opposing magnetic force slows motion without mechanical friction or wear.
    • Induction Motors and Generators: Lenz's law governs the back electromotive force (back-emf) in electric motors, which opposes the supply voltage and limits the operational current as the motor speeds up.
    • Electromagnetic Damping: Sensitive measurement devices, such as galvanometers, use induced currents in conducting frames to quickly bring oscillating needles to rest.