A long insulated copper wire is closely wound as a spiral of ' $N$ ' turns. The spiral has inner radius ' $a$ ' and outer radius ' $b$ '. The spiral lies in the $X-Y$ plane and a steady current ' $I$ ' flows through the wire. The $Z$-component of the magnetic field at the center of the spiral is
A long insulated copper wire is closely wound as a spiral of ' $N$ ' turns. The spiral has inner radius ' $a$ ' and outer radius ' $b$ '. The spiral lies in the $X-Y$ plane and a steady current ' $I$ ' flows through the wire. The $Z$-component of the magnetic field at the center of the spiral is
- [IIT 2011]
- A
$\frac{\mu_0 N I}{2(b-a)} \ln \left(\frac{b}{a}\right)$
- B
$\frac{\mu_0 N I}{2(b-a)} \ln \left(\frac{b+a}{b-a}\right)$
- C
$\frac{\mu_0 N I}{2 b} \ln \left(\frac{b}{a}\right)$
- D
$\frac{\mu_0 N I}{2 b} \ln \left(\frac{b+a}{b-a}\right)$
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