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MHT CET · Physics · Magnetic Effects of Current

Two long parallel wires carrying currents 4 A and 3 A in opposite directions are placed at a distance of 5 cm from each other. A point \(P\) is at equidistance from both the wires such that the line joining the point \(P\) to the wires are perpendicular to each other. The magnitude of magnetic field at point \(P\) is
( \(\mu_0=\) permeability of free space \(=4 \pi \times 10^{-7}\) SI unit)

  1. A \(4 \times 10^{-5} \mathrm{~T}\)
  2. B \(\sqrt{2} \times 10^{-5} \mathrm{~T}\)
  3. C \(2 \times 10^{-5} \mathrm{~T}\)
  4. D \(2 \sqrt{2} \times 10^{-5} \mathrm{~T}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2 \sqrt{2} \times 10^{-5} \mathrm{~T}\)

Step-by-step Solution

Detailed explanation

\(r = \frac{d}{\sqrt{2}} = \frac{0.05}{\sqrt{2}} \, \mathrm{m}\) \(B_1 = \frac{\mu_0 I_1}{2\pi r} = \frac{4\pi \times 10^{-7} \times 4}{2\pi \times (0.05/\sqrt{2})} = 1.6\sqrt{2} \times 10^{-5} \, \mathrm{T}\)