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JEE Main 2022 (27 Jun, Shift 2) · Electric Current, Drift Velocity & Current Density

Electric Current, Drift Velocity & Current Density question from JEE Main 2022 (27 Jun, Shift 2)

Q17JEE Main 2022 · 27 JUN · SHIFT 2Medium

Electric Current, Drift Velocity & Current Density

The current density in a cylindrical wire of radius r = 4.0 mm is 1.0 ×\times 106 A/m2. The current through the outer portion of the wire between radial distances r2\frac{r}{2} and r is xπ\pi A; where x is __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 12

  1. Uniform JJ: I=J×π(r2−r24)=J⋅3πr24I = J \times \pi\left(r^{2} - \dfrac{r^{2}}{4}\right) = J \cdot \dfrac{3\pi r^{2}}{4}
  2. I=106×3π×16×10−64=12π AI = 10^{6} \times \dfrac{3\pi \times 16 \times 10^{-6}}{4} = 12\pi\text{ A}
  3. So x=12x = 12
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