(a) An iron ring of relative permeability μr has windings of insulated copper wire of n turns per metre. When the current in the windings is I, find the expression for the magnetic field in the ring. (b) The susceptibility of a magnetic material is 0.9853. Identify the type of magnetic material. Draw the modification of the field pattern on keeping a piece of this material in a uniform magnetic field.
Answer: (a) B=μrμ0nI. (b) Paramagnetic (small positive susceptibility); it slightly concentrates the field lines.
Solution
(a) The ring acts as a toroid. Applying Ampere's circuital law around the ring, the magnetising field is H=nI, and the magnetic field inside a medium of relative permeability μr is
B=μH=μrμ0H.
Hence
B=μrμ0nI.
(b) The susceptibility χ=0.9853 is positive, so the material is paramagnetic. When placed in a uniform field, a paramagnetic piece draws the field lines slightly inward, so the lines become a little more concentrated inside it.
