Two long, parallel wires each carry the same current i, but the two currents are anti-parallel. the two wires are a distance r apart. what is the magnitude and direction of the magnetic field, b, at a point that is at the midpoint, p, between the two wires?

8 x 10⁻⁷ x  I / r

Explanation:

Two parallel long wires are carrying current I . Let the direction be towards the right in the farthest and towards the left in the nearest. Magnetic field due to current I  at a  distance d is given by the expression

B = μ₀ 2 I / 4π d

I the present case distance d = r/2  

Magnetic field due to one wire at point d = r/2  is

B₁ = μ₀ 2 I / (4π r / 2 )

= 10⁻⁷ x 4I / r

Magnetic field due to the other wire at point d = r/2  is

B₂ = μ₀ 2 I / (4π r / 2 )

= 10⁻⁷ x 4I / r

Direction of magnetic field due to both the wires at the mid  point P will be same . It will be in downward direction in the given scenario

So total magnetic field

B = B₁ + B₂

= 2 x  10⁻⁷ x 4I / r

= 8 x 10⁻⁷ x  I / r