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

`M = 0.71((U_oNI)/(a))`

Step-by-step 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=(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=(U_oIa^2)/(2(x^2+a^2)^(3/2))*2N`

`M=(U_oNa^2I)/((x^2+a^2)^(3/2))`

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

`M=(U_oNIa^2)/(((a^2)/(4)+a^2)^(3/2))`

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

`M = ((4)/(5))^(3/2)((U_oNI)/(a))`

`M = 0.71((U_oNI)/(a))`