A square loop of side 0.4 m and a very long straight wire are placed in the same plane. The straight wire is parallel to one of the sides of the square. A steady current of 5 A flows through the square loop. If the net magnetic field at the exact centre of the square loop is zero, and the perpendicular distance of the long straight wire from the centre of the square loop is 0.4 m, the required magnitude of current in

Step-by-step solution

The magnetic field at the centre of a square loop of side a carrying current I₁ is given by: B_ sq = 4 ₀ I₁ 4 (a/2) ( 45^ + 45^ ) B_ sq = 2 2 ₀ I₁ a Substituting I₁ = 5 A and a = 0.4 m: B_ sq = 2 2 ₀ (5) (0.4) = 10 2 ₀ 0.4 = 25 2 ₀ The magnetic field at a distance d from a very long straight wire carrying current I₂ is: B_ wire = ₀ I₂ 2 d Given the distance from the centre of the square to the long wire is d = 0.4 m: B_ wire = ₀ I₂ 2 (0.4) = ₀ I₂ 0.8 = 5 ₀ I₂ 4 For the net magnetic field at the centre to be zero, t