Two long parallel wires carry currents of 20 a and 5.0 a in opposite directions. the wires are separated by 0.20 m. So, the magnetic field midway between the two wires: 1.5 × 10⁻⁷ T,
Magnetic field at O due to wire 1,
⇒ B₁ = μ₀ I₁ × [tex]\frac{1}{2\pi d}[/tex] , into the paper,
where, d = 0.2 m,
∴ B₁ = μ₀ (20) × [tex]\frac{1}{2\pi (0.2)}[/tex] , into the paper,
Magnetic field at O due to wire 2,
⇒ B₂ = μ₀ I₂ × [tex]\frac{1}{2\pi d}[/tex] , out of the paper,
∴ B₂ = μ₀ (5) × [tex]\frac{1}{2\pi (0.2)}[/tex] , out of the paper,
Thus, net magnetic field at O, B₀ = B₂ - B₁,
⇒ μ₀(20-5) × [tex]\frac{1}{2\pi (0.2)}[/tex] (out of paper),
∴ B₀ = [tex]\frac{(4\pi * 10^{-7)}(-15)}{0.4\pi }[/tex],
⇒ B₀ = - 1.5 × 10⁻⁷ T
Hence, the Magnetic field between two wires, B₀ = - 1.5 × 10⁻⁷ T.
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