Given
Current in the wires,
[tex]\begin{gathered} I_1=5.0\text{ A} \\ I_2=10\text{ A} \end{gathered}[/tex]The distance between the wires,
[tex]d=0.0040\text{ m}[/tex]To find:
The magnetic field between the wires.
Explanation:
Let O be the mid point between the wires.
The magnetic field due to the wire carrying the current
[tex]I_1=5\text{ A}[/tex][tex]\begin{gathered} B_1=\frac{\mu_oI_1}{2\pi(\frac{d}{2})} \\ \Rightarrow B_1=\frac{4\pi\times10^{-7}\times5}{2\pi(\frac{0.0040}{2})} \\ \Rightarrow B_1=2\times10^{-7}\frac{5}{0.002} \\ \Rightarrow B_1=0.0005\text{ T} \end{gathered}[/tex]The magnetic field goes into the plane of the paper.
Again,
The magnetic field due to the wire carrying the current
[tex]I_2=10\text{ A}[/tex][tex]\begin{gathered} B_2=\frac{\mu_oI_2}{2\pi(\frac{d}{2})} \\ \Rightarrow B_2=\frac{4\pi\times10^{-7}\times10}{2\pi\times0.002} \\ \Rightarrow B_2=0.001\text{ T} \end{gathered}[/tex]The magnetic fields goes out of the plane of the paper.
Thus the resultant magnetic field is:
[tex]\begin{gathered} B=B_1-B_2 \\ \Rightarrow B=0.0005-0.001 \\ \Rightarrow B=0.0005\text{ T} \\ \Rightarrow B=-5\times10^{-4}T \end{gathered}[/tex]Conclusion
Thus the required answer is:
[tex]-5\times10^{-4}T[/tex]