Two long parallel wires 20 cm apart carry currents of 5.0 A and 8.0 A in the same direction. Is there any point between the two wires where the magnetic field is zero?

x= 0.077 m from the wire carrying 5.0 A current.

Explanation:

If the wire can be approximated as an infinite one, and we can neglect the diameter of the wire, we can find the magnetic field B at a distance d from the wire, with the following expression:

       

Due to the currents are in the same direction, this means that the magnetic field lines (taking the shape of circumferences) will have opposite directions between the wires.So, if we assume that at some distance from both wires, the magnetic field will be 0, we can write the following equation:

       

where I₁ = 5.0A, I₂= 8.0A and d = 0.2 mSimplifying common terms, we can solve for x, as follows:

       

        ⇒

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