# Help me understand magnetic flux linkage

B=magnetic field strength per unit area
A=Area of conductor moved through the magnetic field
N=Number of coils

I don't understand when my physics text book says the area of a single coil of wire moved through the magnetic field is π×radius of coil^2 as most of the coil is just empty space.

So why does the A include the entier cross section of the coil, including the empty space? Surely empty space moving through a magnetic field has no effect on magnetic flux linkage? Yet the formula includes this empty space.

What is the reason for this?

the reason is due to the concept of flux: it is a scalar product of the vectorial field with the normal vector to the surface.
That is it is important to know how many lines of field pass throught the surface, also if it is empty.

More lines of field enter, more intensive is the magnetic field and its linkage, that is electromagnetic induction, and then more electrons move into the coin.

Thank you for your response Pierce610. What is the normal vector to the surface?

It is a vector perpendicular to a surface which transform a scalar entity, the surface, in a vector.

It means that, like in the static of fluid, it is important that the lines of the fields are parallel to the the normal vector or perpendicular to the surface, it is the same, to transfer a maximum intensity of the field.
If the lines are inclinated it need to modulate (attenuate) the field multiply it by cosinus of the angle due to inclination.
Obviously in this condition the flux, B A cos x, is decreased.

Thank you Pierce610