Question

Two long parallel wires carry equal current i flowing in the same direction and are at a distance 2d apart. The magnetic field at a point lying on the perpendicular bisector joining the wires and at a distance x from the midpoint is:

• A. \( \dfrac{\mu_0 i d}{\pi(d^2 + x^2)} \)
• B. \( \dfrac{\mu_0 i x}{\pi(d^2 - x^2)} \)
• C. \( \dfrac{\mu_0 i x}{(d^2 + x^2)} \)
• D. (mu₀ i d)/((d² + x²))

Hint:

For symmetric current configurations, always resolve magnetic fields into components before adding them.

Answer 1

The Correct Option is A

Step 1: Distance of the point from each wire: r = √(d² + x²)
Step 2: Magnetic field due to one long straight wire: B = (mu₀ i)/(2π r)
Step 3: Only the horizontal components add; vertical components cancel by symmetry. Bₙet = 2 × (mu₀ i)/(2π r) × (d)/(r)
Step 4: Bₙet = (mu₀ i d)/(π(d² + x²))