The approximate formula expressing the inductance of two thin $$co-axial$$ loops of the same radius a when their centres are separated by a distance l with l a is

Question

The approximate formula expressing the inductance of two thin $$co-axial$$ loops of the same radius a when  their centres are separated by a distance l with l > > a is

Infinity Learn · Accepted Answer

Let I $$=$$ current in one loop. This magnetic flux at the centre of the other $$co-axial$$ loop at a distance l from the centre of the first loop $$isB=$$μ$$04$$$$π$$$$2I$$.π$$a2a2+$$ℓ$$23/2The$$ flux through the other loop isϕ$$12=B$$$$π$$$$a2=$$μ$$04$$π⋅$$2$$$$π$$$$a2Ia2+$$ℓ$$23/2$$$$π$$$$a2$$ or ϕ$$12I=$$μ$$04$$π⋅$$2$$$$π$$$$2a42a2+$$ℓ$$23/2=$$ϕ$$0$$$$π$$$$a42a2+$$ℓ$$23/2$$∴μ$$12=M12IM12=$$ϕ$$12I=12$$μ$$0$$$$π$$$$a4$$ℓ$$3($$∵a<<ℓ$$)$$

The approximate formula expressing the inductance of two thin co-axial loops of the same radius a when their centres are separated by a distance l with l > > a is

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