Question
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
Answer: Option C
:
C
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 center due to the ring element
dB=μ0(dN)i2x=μ0i2.Ndx(b−a).1x
∴ Field at the centre
=∫dB=μ0NI2(b−a)b∫adxx
=μ0Ni2(b−a)lnba.
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:
C
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 center due to the ring element
dB=μ0(dN)i2x=μ0i2.Ndx(b−a).1x
∴ Field at the centre
=∫dB=μ0NI2(b−a)b∫adxx
=μ0Ni2(b−a)lnba.
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