Magnetic field at the centre of a loop How is the magnetic field at the centre of a loop of current or a solenoid effected by different cross sectional area?
I understand B=unI gives the magnetic field, but it does not specify how it changes as the area of the coil changes.
Thanks. 
 A: For a solenoid that is much longer than its diameter (if cylindrical), and for points inside the solenoid well away from the ends, the field is uniform all over the cross-section, and lengthways along the solenoid. The value of this field is $B=\mu _{0} \nu I$ in which $\nu$ is the number of turns per unit solenoid length, independently of the diameter or cross-sectional area. [The field becomes seriously non-uniform inside the solenoid within an axial distance of 2 d or so from the ends, d being the solenoid diameter.]
As implied by the formula $B=\mu _{0} \nu I,$ the flux density (field) inside the solenoid and well away from the ends is independent of the cross-sectional area of the solenoid, for a given $\nu$ and $I$, provided that the solenoid remains much longer than its diameter.
For a 'flat coil' things are quite different. The field is non-uniform over the cross-section even within the plane of the coil, and non uniform even along the  axis. At the centre of the coil (of N turns) the field is $B=\frac{\mu _{0}NI}{d}$ in which d is the coil diameter. So, for given values of $N$ and $I$, B is proportional to $\frac {1}{\sqrt A}$.
