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Magnetic flux density - class-XII
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A square loop of side 12 cm and resistance 0.60$\Omega$ is placed vertically in the east-west plane. A uniform magnetic field of 0.1 T is setup across the plane in north-east direction. The magnetic field is decreased to zero in 0.6 s at a steady rate. The magnitude of current during this time interval is
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A
$2.67 \times 10^{-3} A$
💡 Explanation:
Here, Area $A=l^2=(12cm)^2=1.4\times 10^{-2} m^2$
$R=0.60\omega, B _1=0.10 T,\theta=45^0$
$B _2=0,dt=0.6$ s
Initial flux,
$\phi _1=B _1Acos\theta$
$=0.10\times1.4\times10^{-2}\times cos 45^0$
$=9.8\times 10^{-4}$
final flux, $\phi _2$=0
Induced emf,$E=\dfrac{| d\phi |}{dt}=\dfrac{|\phi _2-\phi _1|}{dt}$
Induced emf,$E=\dfrac{| d\phi |}{dt}=\dfrac{|\phi _2-\phi _1|}{dt}$
$E=\dfrac{|9.8\times 10^{-4}|}{0.6}s\,,,,,=1.6\times10^{-3}V$
Current, $I=\dfrac{E}{R}=\dfrac{1.6\times\times 10^{-3}}{0.6}=2.67 \times 10^{-3}$