Question

Two circular loops, of radii R and r (R >> r), respectively, are positioned, parallel to each other, in the yz plane. The centres and axis, of both the loops, lie on the x–axis, a distance x apart. The larger loop has N turns, while the smaller one has n turns, all of the same average radius, in each case. The mutual inductance M, of this pair of loops, for x >> R, equals (nearby)

(1) \(\frac{μ_0 \pi}{2x^3}(\frac{r^2R^2}{nN})\)

(2) \(\frac{μ_0\pi}{2x^2}(nNrR^2)\)

(3) \(\frac{μ_0\pi}{2x^2}(nN)(Rr^2)\)

(4) \(\frac{μ_0\pi}{2x^3}(nr^2)(NR^2)\)

Answer 1

  (4) \(\frac{μ_0\pi}{2x^3}(nr^2)(NR^2)\)

We imagine a current I to flow through the larger loop. The magnetic field, due to it, at the centre of the small loop, would then equal

The small coil has a very small radius. We may, therefore, assume that the magnetic flux, linked with it, is (nearly)