IIT JEE , AIEEE Forum - Physics , Magnetism - i am not getting this electromagnetism qns rates assured those who help me

rakesh61

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the center is

(a)

(b)

(c)

(d)

Please give me a simple detailed solution rates assured

Ans C

madman

magnetic field due to a point in the coil at a distance 2r from the centre = mu * di / 2r
where di is the current throught that element
di = i * d r / (b-a)
where dr is the thickness of a very small part
dB = mu * i * d r / 2r * (b-a)
integrating we have
mu * i/2(b-a) * ln(b/a)

madman

here is the picture

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