Question

N = 2.5.10³ wire turns are uniformly wound on a wooden toroidal core of very small cross-section. A current I flows through the wire. Find the ratio η of the magnetic induction inside the core to that at the centre of the toroid.

Answer 1

Suppose a is the radius of cross section of the core. The winding has a pitch 2πR/N, so the surface current density is

where  is a unit vector along the cross section of the core and  is a unit vector along its length. 

The magnetic field inside the cross section of the core is due to first term above, and is given by

(NI is total current due to the above surface current (first term.))

Thus,  

The magnetic field at the centre of the core can be obtained from the basic formula.

The ratio of the two magnetic field, is = N/π