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

B_{above} = μI_{0} / 2πr

here, r = a +a/2, so

B_{above }= μI_{0} / 2π(a +a/2)

thus,

B_{above }= μI_{0} / 3πa......................(1)

and

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

B_{below} = μI_{0}r / 2πa^{2}

here, r = a/2

B_{below }= μI_{0}(a/2)/ 2πa^{2}

thus,

B_{below }= μI_{0} / 4πa......................(1)

.

now, the ratio will be given as

B_{above }/ B_{below} = (μI_{0} / 3πa) / ( μI_{0} / 4πa)

thus, we get

**B**_{above }**/ B**_{below}** = 4/3**

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