A conducting circular loop made of a thin wire, has area 3.5 × 10 - 3 m2 and resistance 10 Ω. It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50 π t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to: (a) 0.14 mC (b) 0.7 mC (c) 0.21 mC (d) 0.6 mC

Answer: (a). At t = 0: B = 0. At t = 10 ms: B = 0.4sin (50π × 0.01) = 0.4sin π/2 = 0.4 T. Δφ = 0.4 × 3.5 × 10⁻³ = 1.4 × 10⁻³ Wb q = (Δφ)/(R) = 1.4 × 10⁻³10 = 1.4 × 10⁻⁴ C So the answer is (a) 0.14 mC.

A conducting circular loop made of a thin wire, has area 3.5 × 10 - 3… | JEE Main 2019 (9 Jan, Shift 1)

Q74JEE Main 2019 · 9 JAN · SHIFT 1Medium

Magnetic Flux & Faraday's Law

A conducting circular loop made of a thin wire, has area 3.5 $\times$ 10 $-$ 3 m2 and resistance 10 $\Omega$ . It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50 $\pi$ t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to:

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Answer: (a)

At $t = 0$ : $B = 0$ . At $t = 10$ ms: $B = 0.4\sin(50\pi \times 0.01) = 0.4\sin\frac{\pi}{2} = 0.4$ T.
$\Delta\phi = 0.4 \times 3.5 \times 10^{-3} = 1.4 \times 10^{-3}$ Wb
$q = \frac{\Delta\phi}{R} = \frac{1.4 \times 10^{-3}}{10} = 1.4 \times 10^{-4}$ C
So the answer is (a) 0.14 mC.

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