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JEE Main 2023 (25 Jan, Shift 2) · Magnetic Field of Straight Wires

Magnetic Field of Straight Wires question from JEE Main 2023 (25 Jan, Shift 2)

Q40JEE Main 2023 · 25 JAN · SHIFT 2Medium

Magnetic Field of Straight Wires

Two long parallel wires carrying currents 8A and 15A in opposite directions are placed at a distance of 7 cm from each other. A point P is equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P is _____________ ×10−6\times 10^{-6} T.

(Given: 2=1.4\sqrt{2} = 1.4)

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

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Answer: 68

  1. r=72=5 cmr = \frac{7}{\sqrt{2}} = 5\text{ cm} (with 2=1.4\sqrt{2} = 1.4).
  2. B1=2×10−7×80.05=32 μTB_1 = \frac{2 \times 10^{-7} \times 8}{0.05} = 32\ \mu\text{T}, B2=2×10−7×150.05=60 μTB_2 = \frac{2 \times 10^{-7} \times 15}{0.05} = 60\ \mu\text{T}
  3. The fields are perpendicular: B=322+602=68×10−6 TB = \sqrt{32^2 + 60^2} = 68 \times 10^{-6}\text{ T}
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