Electromagnetic Induction Question 5
Question 5 - 2024 (29 Jan Shift 1)
A square loop of side $10 \mathrm{~cm}$ and resistance $0.7 \Omega$ is placed vertically in east-west plane. A uniform magnetic field of $0.20 \mathrm{~T}$ is set up across the plane in north east direction. The magnetic field is decreased to zero in $1 \mathrm{~s}$ at a steady rate. Then, magnitude of induced emf is $\sqrt{\mathrm{x}} \times 10^{-3} \mathrm{~V}$. The value of $x$ is
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Answer: (2)
Solution:
$$ \begin{aligned} & \overrightarrow{\mathrm{A}}=(0.1)^{2} \hat{\mathrm{j}} \ & \overrightarrow{\mathrm{B}}=\frac{0.2}{\sqrt{2}} \hat{\mathrm{i}}+\frac{0.2}{\sqrt{2}} \hat{\mathrm{j}} \end{aligned} $$
Magnitude of induced emf
$\mathrm{c}=\frac{\Delta \phi}{\Delta \mathrm{t}}=\frac{\overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{A}}-0}{\mathrm{l}}=\sqrt{2} \times 10^{-3} \mathrm{~V}$
