The changing flux in the line links the loop and hence the line has
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Answer:
In circuit theory, flux linkage is a property of a two-terminal element. It is an extension rather than an equivalent of magnetic flux and is defined as a time integral[citation needed]
{\displaystyle \lambda =\int {\mathcal {E}}\,dt,}{\displaystyle \lambda =\int {\mathcal {E}}\,dt,}
where {\displaystyle {\mathcal {E}}}{\mathcal {E}} is the voltage across the device, or the potential difference between the two terminals. This definition can also be written in differential form as a rate
{\displaystyle {\mathcal {E}}={\frac {d\lambda }{dt}}.}{\displaystyle {\mathcal {E}}={\frac {d\lambda }{dt}}.}
Faraday showed that the magnitude of the electromotive force (EMF) generated in a conductor forming a closed loop is proportional to the rate of change of the total magnetic flux passing through the loop (Faraday's law of induction). Thus, for a typical inductance (a coil of conducting wire), the flux linkage is equivalent to magnetic flux, which is the total magnetic field passing through the surface (i.e., normal to that surface) formed by a closed conducting loop coil and is determined by the number of turns in the coil and the magnetic field, i.e.,
{\displaystyle \lambda =\int \limits _{S}{\vec {B}}\cdot d{\vec {S}},}{\displaystyle \lambda =\int \limits _{S}{\vec {B}}\cdot d{\vec {S}},}
where {\displaystyle {\vec {B}}}{\vec {B}} is the flux density, or flux per unit area at a given point in space.
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