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)
thus,
Babove = μI0 / 3πa......................(1)
and
magnetic field at 'a/2' below the surface of the wire
Bbelow = μI0r / 2πa2
here, r = a/2
Bbelow = μI0(a/2)/ 2πa2
thus,
Bbelow = μI0 / 4πa......................(1)
.
now, the ratio will be given as
Babove / Bbelow = (μI0 / 3πa) / ( μI0 / 4πa)
thus, we get
Babove / Bbelow = 4/3