Answer:
The magnitude of the magnetic field at the point of interest is B=1.8·10^-3T
Explanation:
To solve this problem we can calculate the expression of the magnetic field for one of the coils and using the symmetry of the problem we can use twice this expression to obtain the expression of the total field as:
[tex]B_{T}=B_{1}+B_{2}[/tex]
For the magnetic field [tex]B{1}[/tex] we use the Biot-Savart law:
[tex]d\vec{B}=\frac{\mu_{0}i\vec{dl}}{4\pi}\times \frac{\vec{r}-\vec{r'}}{|\vec{r}-\vec{r'}|^3}[/tex]
Using cylindrical coordinates, the expression of the magnetic field in a circular coil is:
[tex]B_{i}=\frac{\mu_{0}ir^2}{2(\sqrt{z^2+r^2})^3}[/tex]
The expression of the magnetic field in a circular coil with N turns is:
[tex]B_{i}=\frac{\mu_{0}iNr^2}{2(\sqrt{z^2+r^2})^3}[/tex]
Because we have a point of symmetry in the middle between the 2 coils, the expression of the field in that point is:
[tex]B_{T}=B_{1}+B_{2}=\frac{\mu_{0}iNr^2}{(\sqrt{z^2+r^2})^3}[/tex]
with r=0.5m, Z=0.25m, i=10A and N=100
