Prove that lenz formula
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Lenz's law (pronounced /ˈlɛnts/), named after the physicist Emil Lenz who formulated it in 1834,[1] states that the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field. Or as informally, yet concisely summarised by D.J. Griffiths:
Nature abhors a change in flux.[2]
Lenz's law is shown by the negative sign in Faraday's law of induction:
{\displaystyle {\mathcal {E}}=-{\frac {\partial \Phi _{\mathbf {B} }}{\partial t}},}

which indicates that the induced electromotive force {\displaystyle {\mathcal {E}}} and the rate of change in magnetic flux {\displaystyle \Phi _{\mathbf {B} }} have opposite signs.[3] It is a qualitative law that specifies the direction of induced current but says nothing about its magnitude. Lenz's law explains the direction of many effects in electromagnetism, such as the direction of voltage induced in an inductoror wire loop by a changing current, or why eddy currents exert a drag force on moving objects in a magnetic field.
Lenz's law can be seen as analogous to Newton's third law in classic mechanics.[4]
For a rigorous mathematical treatment, see electromagnetic induction and M
Nature abhors a change in flux.[2]
Lenz's law is shown by the negative sign in Faraday's law of induction:
{\displaystyle {\mathcal {E}}=-{\frac {\partial \Phi _{\mathbf {B} }}{\partial t}},}

which indicates that the induced electromotive force {\displaystyle {\mathcal {E}}} and the rate of change in magnetic flux {\displaystyle \Phi _{\mathbf {B} }} have opposite signs.[3] It is a qualitative law that specifies the direction of induced current but says nothing about its magnitude. Lenz's law explains the direction of many effects in electromagnetism, such as the direction of voltage induced in an inductoror wire loop by a changing current, or why eddy currents exert a drag force on moving objects in a magnetic field.
Lenz's law can be seen as analogous to Newton's third law in classic mechanics.[4]
For a rigorous mathematical treatment, see electromagnetic induction and M
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