Mutual induction =\\frac {Flux through PQRS}{Current through AB} \\phi=B\\cdot A A=cdx B=\\frac {\\mu_0I}{2\\pi x} d\\phi=\\frac {\\mu_0I}{2\\pi x}cdx \ herefore \\phi=\\frac {\\mu_0Ic}{2\\pi}\\int_{a}^{b}\\frac {dx}{x} =\\frac {\\mu_0Ic}{2\\pi}ln(\\frac {b}{a}) \ herefore m=\\frac {\\mu_0c}{2\\pi}ln(\\frac {b}{a})