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 magneti

Question

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 _______.

TestHub · Accepted Answer

The area vector for the square loop is given by

$\vec{A} = (0.1)^{2} \hat{j} m^{2}$

According to the above diagram, the magnetic field is given by

$\vec{B} = \frac{0.2}{\sqrt{2}} \hat{i} + \frac{0.2}{\sqrt{2}} \hat{j}$

Hence, the magnitude of induced emf can be calculated as follows

$\begin{array}{rcl} e & = & \frac{Δ ϕ}{Δ t} \\ = & \frac{\vec{B} \cdot \vec{A} - 0}{1} \\ = & \frac{(\frac{0.2}{\sqrt{2}} \hat{i} + \frac{0.2}{\sqrt{2}} \hat{j}) \cdot ((0.1)^{2} \hat{j}) - 0}{1} V \\ = & \sqrt{2} \times 10^{- 3} V \end{array}$

Hence, $x = 2$ .

Physics - EMI/AC Question with Solution | TestHub

Doubts & Discussion