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**Hint:**The total number of magnetic lines of force passing normally through an area placed in a magnetic field is equal to the magnetic flux linked with that area. The process by which an emf is induced in a circuit by the virtue of changing the magnetic field around it is known as electromagnetic induction.

**Complete step by step answer:**

**Magnetic Field$\left( B \right)$:**A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. This magnetic field can be seen as imaginary lines known as the magnetic field lines.

**Magnetic Flux $\left( \varphi \right)$:**The total number of magnetic lines of force passing normally through an area$\left( A \right)$ placed in a magnetic field$\left( B \right)$ is equal to the magnetic flux linked with that area. That is,

$\varphi = \oint {\overrightarrow B .d\overrightarrow A } $

The SI unit of magnetic flux is weber$\left( {Wb} \right)$.

Faraday’s Laws of Electromagnetic Induction:

**First Law:**Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit changes, an emf called induced emf is produced in the circuit. The induced emf persists as long as there is change of flux.

**Second Law:**The induced emf $\left( \varepsilon \right)$ is given by the rate of change of magnetic flux linked with the circuit. That is,

$\varepsilon = - \dfrac{{d\varphi }}{{dt}}$

For $N$ turns, $\varepsilon = - \dfrac{{Nd\varphi }}{{dt}}$.

So, in the above case,

$\varepsilon = - \dfrac{{50 \times d\left( {0.02\cos 100\pi t} \right)}}{{dt}}$

$ \Rightarrow \varepsilon = - 50 \times \left( {0.02} \right) \times \left\{ { - \sin 100\pi t} \right\} \times 100\pi $

$ \Rightarrow \varepsilon = 100\pi \sin 100\pi t$

For maximum emf, $\sin 100\pi t = 1$. So,

$ \Rightarrow \varepsilon = 100 \times 3.14$

$\therefore \varepsilon = 314volt$

**Thus, the correct answer is option A.**

**Note:**Since magnetic flux is the dot product of magnetic field vector and areal vector, therefore magnetic flux is a scalar quantity. As soon as the magnetic flux stops changing the induced emf returns to zero.

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