Answer:
[tex]M = 0.71(\frac{U_oNI}{a})[/tex]
Explanation:
The magnitude of the magnetic field at a point P, a distance a/2 from the center of the each coil can be determined as follows;
Let the magnitude be M;
[tex]M=\frac{U_oIa^2}{2(x^2+a^2)^{3/2}}[/tex]
Note that there is a total of 2N turns in the two coils.
So, we have:
[tex]M=\frac{U_oIa^2}{2(x^2+a^2)^{3/2}}*2N[/tex]
[tex]M=\frac{U_oNa^2I}{(x^2+a^2)^{3/2}}[/tex]
where x = distance (d) which is given as a/2; we have:
[tex]M=\frac{U_oNIa^2}{(\frac{a^2}{4}+a^2)^{3/2}}[/tex]
[tex]M=\frac{U_oNIa^2}{{a^3}(\frac{5}{4})^{3/2}}[/tex]
[tex]M = (\frac{4}{5})^{3/2}(\frac{U_oNI}{a})[/tex]
[tex]M = 0.71(\frac{U_oNI}{a})[/tex]
