Q14 of 26 Page 1

(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.

a) According to ampere’s law, the line integral of magnetic field B around any closed circuit is equal to μo times the total current passing through this closed circuit. Mathematically,


∫B.dl = μoμrIenclosed


Now ∫B.dl = B∫dl = BL , if B is constant and directed along the tangent to every point on the perimeter L of a closed curve.


For the field inside the ring, we can write


∫B.dl = B∫dl = B. 2πr


(r = radius of the ring)


Also, Ienclosed = (2πrn)I using equation (i)


Where n = number of turns per meter


∴ B. 2πr = μoμr (n. 2πr)I


∴ B = μoμrnI


b) The susceptibility of this material is between 0 and 1. So it is a paramagnetic material.



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