A square loop of side 10 cm and resistance 0.7 is placed vertically in east-west plane. A uniform magnetic field of 0.20T is set up across the plane in northeast direction. The magnetic field is decreased to zero in 1s at a steady rate. Then, magnitude of

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Solution

Q.
A square loop of side 10 cm and resistance 0.7 $Ω$ is placed vertically in east-west plane. A uniform magnetic field of 0.20T is set up across the plane in northeast direction. The magnetic field is decreased to zero in 1s at a steady rate. Then, magnitude of induced emf is $\sqrt{x} \times 10^{- 3}$ V. The value of $x$ is ______. [2024]

Ans.
(2)

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

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

Magnitude of induced emf

$e = \frac{Δ ϕ}{Δ t} = \frac{\vec{B} \cdot \vec{A} - 0}{1} = \sqrt{2} \times 10^{- 3} V$

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