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Electromagnetic Induction — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsElectromagnetic Induction3 Marks
Question
A square wire loop with sides $0.5 m$ is placed with its plane perpendicular to a magnetic field. The resistance of the loop is $5 \Omega$. Find at what rate the magnetic induction should be changed so that a current of $0.1 A$ is induced in the loop.
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Answer

Data : $|=0.5 m , R =5 \Omega|=,0.1 A$
$A=l^2=0.5 \times 0.5=0.25 m ^2$
The magnitude of the induced emf,
$| e |=\frac{d F }{d t}=\frac{d}{d t}( BA )= A \frac{d B}{d t}$
since the area (A) of the coil is constant. The induced current, $\mid=\frac{|e|}{R}=\frac{A}{R} \frac{d B}{d t}$
$\therefore$ The time rate of change of magnetic induction,
$\frac{d B}{d t}=\frac{I R}{A}=\frac{0.1 \times 5}{0.25}=2 T / s$

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