JEE Advanced 2020 Concept Recapitulation Test 2 Paper 1

Let n be the number of turns per unit length along the radii of the spiral. Consider a ring of radii x and x+dx.
Number of turns in the ring =ndx
∴ Magnetic field at the center due to this ring =‌

µ0(ndx)i

2x

∴B(‌ total field ‌) =

b

∫

a

‌

µ0nidx

2x

=‌

1

2

µ0ni‌ln‌

b

a

But ‌‌n=‌

N

b−a

B‌‌=‌

µ0Ni

2(b−a)

‌ln‌

b

a

=‌

4π×10−7×100×8×10−3

2(10−5)×10−2

‌ln‌

10

5

‌‌=6.9×10−6T=6.9µT.