A square loop of side 10 cm and resistance 0 . 7 Ω is placed vertically in the east-west plane. A uniform magnetic field of 0 . 20 T is set up across the plane in the north-east direction. The magnetic field is decreased to zero in 1 s at a steady rate. Then, the magnitude of induced emf is x × 10 - 3 V . The value of x is _______.

Step-by-step solution

The area vector for the square loop is given by A → = ( 0 . 1 ) 2 j ^ m 2 According to the above diagram, the magnetic field is given by B → = 0 . 2 2 i ^ + 0 . 2 2 j ^ Hence, the magnitude of induced emf can be calculated as follows e = Δ ϕ Δ t = B → · A → - 0 1 = 0 . 2 2 i ^ + 0 . 2 2 j ^ · ( 0 . 1 ) 2 j ^ - 0 1 V = 2 × 10 - 3 V Hence, x = 2 .