Faraday's law, induced emf and current

A square loop of side 1 m and resistance \(1\,\Omega\) is placed in a magnetic field of 0.5 T. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is :

A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 rad \(\text{s}^{-1}\). If the vertical component of earth's magnetic field at that place is \(2 \times 10^{-5}\) T and electrical resistance of the coil is \(12.56\,\Omega\), then the maximum induced current in the coil will be :

A 800 turn coil of effective area 0.05 m\(^2\) is kept perpendicular to a magnetic field \(5\times10^{-5}\) T. When the plane of the coil is rotated by \(90^\circ\) around any of its coplanar axis in 0.1 s, the emf induced in the coil will be :

A uniform magnetic field is restricted within a region of radius \(r\). The magnetic field changes with time at a rate \(\frac{d\vec B}{dt}\). Loop 1 of radius \(R>r\) encloses the region \(r\) and loop 2 of radius \(R\) is outside the region of magnetic field as shown in the figure below. Then the e.m.f. generated is