What is the mutual inductance of a two-loop s | vedclass

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(D) The magnetic field $B_1$ at the center of coil $(2)$ due to a current $i$ in coil $(1)$ is given by the formula for the magnetic field of a magnet

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$\frac{{\mu _0}\pi {a^4}}{{2{l^3}}}$

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(D) The magnetic field $B_1$ at the center of coil $(2)$ due to a current $i$ in coil $(1)$ is given by the formula for the magnetic field of a magnetic dipole at an axial distance $l$:$B_1 = \frac{{\mu _0}}{4\pi} \cdot \frac{2m}{l^3}$where the magnetic moment $m = iA = i(\pi a^2)$.Substituting $m$ into the expression for $B_1$:$B_1 = \frac{{\mu _0}}{4\pi} \cdot \frac{2(i\pi a^2)}{l^3} = \frac{{\mu _0} i a^2}{2l^3}$The magnetic flux $\phi_2$ linked with coil $(2)$ is:$\phi_2 = B_1 A_2 = \left( \frac{{\mu _0} i a^2}{2l^3} \right) (\pi a^2) = \frac{{\mu _0} \pi i a^4}{2l^3}$Since $\phi_2 = Mi$,the mutual inductance $M$ is:$M = \frac{{\mu _0} \pi a^4}{2l^3}$

What is the mutual inductance of a two-loop system as shown with centre separation $l$ where $l >> a$?

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