Question

a current I is flowing along an infinite straight wire in the positive direction and same current is flowing along a similar parallel wires 5 metre apart in the negative Z direction a point P is at a perpendicular distance 3 metre from the first wire and 4 metres from the second. what will be the magnitude of the magnetic field B at point P​

Answer 1

The magnitude of the magnetic field B at point P​ is 5/24π (μ₀I)

Explanation:

The magnetic field at the first wire is given by the formula:

B₁ = (μ₀I)/(2πR₁)

⇒ B₁ = (μ₀I)/(2π × 3)

The magnetic field at the second wire is given by the formula:

B₂ = (μ₀I)/(2πR₂)

⇒ B₂ = (μ₀I)/(2π × 4)

The net magnetic field is given as:

B = √(B₁² + B₂²)

on substituting the values, we get,

B = (μ₀I)/(2π) √(1/9 + 1/16)

B = (μ₀I × 5)/(2π × 3 × 4)

B = 5/24 (μ₀I)/π

∴ B = 5/24π (μ₀I)