Question

Use the expression for the magnetic field of a loop to find an expression for the magnitude of the magnetic field at point P, a distance a/2 from the center of each coil Note that there is a total of 2N turns in the two coils.

Answer 1

Answer:

$M = 0.71(\frac{U_oNI}{a})$

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;

$M=\frac{U_oIa^2}{2(x^2+a^2)^{3/2}}$

Note that there is a total of 2N turns in the two coils.

So, we have:

$M=\frac{U_oIa^2}{2(x^2+a^2)^{3/2}}*2N$

$M=\frac{U_oNa^2I}{(x^2+a^2)^{3/2}}$

where x = distance (d) which is given as a/2; we have:

$M=\frac{U_oNIa^2}{(\frac{a^2}{4}+a^2)^{3/2}}$

$M=\frac{U_oNIa^2}{{a^3}(\frac{5}{4})^{3/2}}$

$M = (\frac{4}{5})^{3/2}(\frac{U_oNI}{a})$

$M = 0.71(\frac{U_oNI}{a})$