# Magnetic Field Density

temujin
Hi

My textbook denotes the magnetic flux through a single turn loop as $$\Phi$$, and the magnetic flux density in the same loop as $$B = \frac{\Phi}{Area}$$.

Extending to an N-turn loop the total flux passing through the coil is given by $$\Psi = N\cdot\Phi \leftrightarrow \Phi = \frac{\Psi}{N}$$ .
Inserted into the equation for B this would produce: $$B=\frac{\Psi}{Area\cdot N}$$

Which means that for a given flux, the flux density would be lower with a high number of turns...!
Can this be right?

Should not the flux density be the total flux passing through the coil divided by the Area of the coil surface...and that increasing N should increase magnetic flux and magnetic flux density...? ?

regards
t.