State the lanz law and show that it is in accordance with the law of conservation of energy
Answers
Lenz's law states that the current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the motion.
Lenz's law is contained in the rigorous treatment of Faraday's law of induction, where it finds expression by the negative sign:
{\displaystyle {\mathcal {E}}=-{\frac {\partial \Phi _{\mathbf {B} }}{\partial t}},}
{\displaystyle {\mathcal {E}}=-{\frac {\partial \Phi _{\mathbf {B} }}{\partial t}},}
which indicates that the induced electromotive force {\displaystyle {\mathcal {E}}}{\mathcal {E}} and the rate of change in magnetic flux {\displaystyle \Phi _{\mathbf {B} }}{\displaystyle \Phi _{\mathbf {B} }} have opposite signs.[3]
This means that the direction of the back EMF of an induced field opposes the changing current that is its cause. D.J. Griffiths summarized it as follows: Nature abhors a change in flux.[4]
If a change in the magnetic field of current i1 induces another electric current, i2, the direction of i2 is opposite that of the change in i1. If these currents are in two coaxial circular conductors ℓ1 and ℓ2 respectively, and both are initially 0, then the currents i1 and i2 must counter-rotate. The opposing currents will repel each other as a result.
Magnetic fields from strong magnets can create counter-rotating currents in a copper or aluminum pipe. This is shown by dropping the magnet through the pipe. The descent of the magnet inside the pipe is observably slower than when dropped outside the pipe.
When a voltage is generated by a change in magnetic flux according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. In the examples below, if the flux is increasing, the induced field acts in opposition to it. If it is decreasing, the induced field acts in the direction of the applied field to oppose the change.
