a straight long thick wire of uniform cross section of radius 'a' is carrying a steady current I.use ampere's circuital law to obtain a relation showing the variation of magnetic field (B) inside the wire with distance r , (r<=a) and(r>a) of the field point from the center of its cross section .Plot a graph showing the nature of this variation.

Calculate the ratio of the magnetic field at a point a/2 above the surface of the wire to that at a point a/2 below its surface.What is the max value of the field of this wire?

(i) For r < a


(ii) For r > a


Variation of magnetic field 'B' with distance 'r'


magnetic field at 'a/2' above the surface of wire

Babove = μI0 / 2πr 

here, r = a  +a/2, so

Babove = μI0 / 2π(a  +a/2)


Babove = μI0 / 3πa......................(1)


magnetic field at 'a/2' below the surface of the wire

Bbelow = μI0r / 2πa2 

here, r = a/2

Bbelow = μI0(a/2)/ 2πa2


Bbelow = μI0 / 4πa......................(1)


now, the ratio will be given as

Babove / Bbelow  =  (μI0 / 3πa) / ( μI0 / 4πa)

thus, we get

Babove / Bbelow  = 4/3

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