Faradey's law states that the EMF induced by a change in magnetic flux depends on the change in (Faraday's law). dt magnetic flux with respect to time and number of turns of coils. Mathematically it is defined like the figure. Why do we use ds in the line integral of Faradey's law to calculate the electric field?

Faradey's law states that the EMF induced by a change in magnetic flux depends on the change in (Faraday's law). dt magnetic flux with respect to time and number of turns of coils. Mathematically it is defined like the figure. Why do we use ds in the line integral of Faradey's law to calculate the electric field?

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