Question 33 of 153

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of $4mm$ and a total length of $30cm.$ The magnetic field changes with time at a steady rate $dB/dt=0.032{Ts}^{-1}.$ The induced current in the $loop$is close to (Resistivity of the metal wire is $1.23\times {10}^{-8}\Omega m$ )

A0.43 AB0.61 AC0.34 AD0.53 A

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Answer: (B) 0.61 A

Radius $=d/2=2mm$
${R}_{wire}=\dfrac{\rho l}{A}$
$\phi =BA;\left|e\right|=\dfrac{d\phi }{dt}=\dfrac{dB}{dt}\left(A\right)$
$i=\dfrac{e}{R}=\left|\dfrac{dB}{dt}\right|\dfrac{{\left(A\right)}^{2}}{\rho l}=\dfrac{0.032\times {\left\{\pi \times 2\times {10}^{-3}\right\}}^{2}}{1.23\times {10}^{-8}\times 4\times 0.3}$
$=0.61A$