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 positive and lies between 0 and 1. So it is a paramagnetic material. When a paramagnetic substance is placed in a uniform magnetic field the unpaired electron aligns itself with the external field.
The modified magnetic field when a paramagnetic material is placed in a uniform magnetic field is shown below.
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