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
A
μ0NIb
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B
2μ0NIa
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C
μ0NI2(b−a)lnba
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D
μ0IN2(b−a)lnba
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Solution
The correct option is Cμ0NI2(b−a)lnba
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 element dB=μ0(dN)i2x=μ0i2.Ndx(b−a).1x ∴ Field at the centre =∫dB=μ0Ni2(b−a)∫badxx =μ0Ni2(b−a) In ba