A uniform magnetic field B exists in a direction perpendicular

Question:

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 $4 \mathrm{~mm}$ and a total length of $30 \mathrm{~cm}$. The magnetic field changes with time at a steady rate $\mathrm{dB} / \mathrm{dt}=0.032 \mathrm{Ts}^{-1}$.The induced current in the loop is close to

(Resistivity of the metal wire is $1.23 \times 10^{-8} \Omega \mathrm{m}$ )

  1. $0.61 \mathrm{~A}$

  2. $0.34 \mathrm{~A}$

  3. $0.43 \mathrm{~A}$

  4. $0.53 \mathrm{~A}$


Correct Option: 1,

Solution:

$\mathrm{q}_{\mathrm{i}}=\frac{\mathrm{d}\left(\mathrm{Ba}^{2}\right)}{\mathrm{dt}}=\mathrm{a}^{2} \frac{\mathrm{dB}}{\mathrm{dt}}$

$\mathrm{i}=\frac{\mathrm{q}}{\mathrm{R}}=\frac{\mathrm{a}^{2} \mathrm{~dB} / \mathrm{dt}}{\frac{\rho(40)}{\pi \mathrm{r}^{2}}}$

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