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 centre is

Question

Infinity Learn · Accepted Answer

Number of turns per unit width $$=$$  Nb−a. Consider an elemental ring of radius x and with thickness dx Number of turns in the ring $$=$$ $$dN=$$ Ndxb−a. Magnetic field at the centre due to the ring $$elementdB=$$μ$$0dNi2x$$  $$=$$ μ$$0i2$$  Ndxb−a .  $$1x$$∴    Field  at  the  centre∴    Field  at  the  $$centre=$$ ∫dB $$=$$ μ$$0Ni2b$$−a  ∫ab $$dxx=$$μ$$0Ni2b$$−a  ln  ba.

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 centre is

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