Lenz's law

Examples of Lenz's law in the following topics:

• Faraday's Law of Induction and Lenz' Law

  • The minus means that the EMF creates a current I and magnetic field B that oppose the change in flux Δthis is known as Lenz' law.
  • The direction (given by the minus sign) of the EMF is so important that it is called Lenz' law after the Russian Heinrich Lenz (1804–1865), who, like Faraday and Henry, independently investigated aspects of induction.
  • Lenz' law is a manifestation of the conservation of energy.
  • Lenz' law is a consequence.
  • This is one aspect of Lenz's law—induction opposes any change in flux.

• Mechanical Work and Electrical Energy

  • We learned in the Atom "Faraday's Law of Induction and Lenz' Law" that Lenz' law is a manifestation of the conservation of energy.
  • As we see in the example in this Atom, Lenz' law guarantees that the motion of the rod is opposed because of nature's tendency to oppose a change in magnetic field.
  • (b) Lenz's law gives the directions of the induced field and current, and the polarity of the induced emf.
  • Apply the law of conservation of energy to describe the production motional electromotive force with mechanical work

• Inductance

  • Mutual inductance is the effect of Faraday's law of induction for one device upon another, such as the primary coil in transmitting energy to the secondary in a transformer.
  • The minus sign is an expression of Lenz's law.
  • Self-inductance, the effect of Faraday's law of induction of a device on itself, also exists.
  • When, for example, current through a coil is increased, the magnetic field and flux also increase, inducing a counter emf, as required by Lenz's law.
  • Again, the minus sign is an expression of Lenz's law, indicating that emf opposes the change in current.

• Motional EMF

  • When flux changes, an EMF is induced according to Faraday's law of induction.
  • To find the magnitude of EMF induced along the moving rod, we use Faraday's law of induction without the sign:
  • To find the direction of the induced field, the direction of the current, and the polarity of the induced EMF we apply Lenz' law, as explained in Faraday's Law of Induction: Lenz' Law.
  • (b) Lenz's law gives the directions of the induced field and current, and the polarity of the induced emf.

• Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams

  • In an AC circuit with an inductor, the voltage across an inductor "leads" the current because of the Lenz' law.
  • The rms current Irms through an inductor L is given by a version of Ohm's law: $I_{rms} = \frac{V_{rms}}{X_L}$ where Vrms is the rms voltage across the inductor and $X_L = 2\pi \nu L$ with $\nu$ the frequency of the AC voltage source in hertz.
  • The voltage across an inductor "leads" the current because of the Lenz's law.

• Inductance

  • From Lenz's law, a changing electric current through a circuit that has inductance induces a proportional voltage which opposes the change in current (if this wasn't true one can easily see how energy could not be conserved, with a changing current reinforcing the change in a positive feedback loop).
  • The minus sign is an expression of Lenz's law.
  • Self-inductance, the effect of Faraday's law of induction of a device on itself, also exists.
  • When, for example, current through a coil is increased, the magnetic field and flux also increase, inducing a counter emf, as required by Lenz's law.
  • The minus sign is an expression of Lenz's law, indicating that emf opposes the change in current.

• RLC Series Circuit: At Large and Small Frequencies; Phasor Diagram

  • By combining Ohm's law (Irms=Vrms/Z; Irms and Vrms are rms current and voltage) and the expression for impedance Z, from:
  • This response makes sense because, at high frequencies, Lenz's law suggests that the impedance due to the inductor will be large.

• RL Circuits

  • Mutual inductance is the effect of Faraday's law of induction for one device upon another, while self-inductance is the the effect of Faraday's law of induction of a device on itself.
  • We know from Lenz's law that inductors oppose changes in current.
  • The change in current changes the magnetic flux, inducing an emf opposing the change (Lenz's law).

• Back EMF, Eddy Currents, and Magnetic Damping

  • Back EMF, eddy currents, and magnetic damping are all due to induced EMF and can be explained by Faraday's law of induction.
  • When the coil of a motor is turned, magnetic flux changes, and an electromotive force (EMF), consistent with Faraday's law of induction, is induced.
  • Lenz' law tells us the induced EMF opposes any change, so that the input EMF that powers the motor will be opposed by the motor's self-generated EMF, called the back EMF of the motor.
  • As it enters from the left, flux increases, and so an eddy current is set up (Faraday's law) in the counterclockwise direction (Lenz' law), as shown.

• Gauss's Law

  • Gauss's law is a law relating the distribution of electric charge to the resulting electric field.
  • Gauss's law can be used to derive Coulomb's law, and vice versa.
  • In fact, Gauss's law does hold for moving charges, and in this respect Gauss's law is more general than Coulomb's law.
  • Gauss's law has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity.
  • In fact, any "inverse-square law" can be formulated in a way similar to Gauss's law: For example, Gauss's law itself is essentially equivalent to the inverse-square Coulomb's law, and Gauss's law for gravity is essentially equivalent to the inverse-square Newton's law of gravity.