Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/84

separating two media, then if V, V' are the potentials in the two media, the magnetic forces towards the surface in the two media are ${\frac {dV}{d\nu }}$ and ${\frac {dV'}{d\nu '}}$.

The quantities of magnetic induction through the element of surface dS are $\mu {\frac {dV}{d\nu }}dS$ and $\mu '{\frac {dV'}{d\nu '}}dS$ in the two media respectively reckoned towards dS.

Since the total flux towards dS is zero,

$\mu {\frac {dV}{d\nu }}+\mu '{\frac {dV'}{d\nu '}}=0.$

But by the theory of the potential near a surface of density σ,

${\frac {dV}{d\nu }}+{\frac {dV'}{d\nu '}}+4\pi \sigma =0.$

Hence

${\frac {dV}{d\nu }}\left(1-{\frac {\mu }{d\mu '}}\right)+4\pi \sigma =0.$

If κ₁ is the ratio of the superficial magnetization to the normal force in the first medium whose coefficient is μ, we have

$4\pi \kappa _{1}={\frac {\mu -\mu '}{\mu '}}.$

Hence κ₁ will be positive or negative according as μ is greater or less than μ'. If we put μ = 4πκ + 1 and μ' = 4πκ' + 1,

$\kappa _{1}={\frac {\kappa -\kappa _{1}}{4\pi \kappa +1}}.$

In this expression κ and κ' are the coefficients of induced magnetization of the first and second medium deduced from experiments made in air, and κ₁ is the coefficient of induced magnetization of the first medium when surrounded by the second medium.

If κ' is greater than κ, then κ₁ is negative, or the apparent magnetization of the first medium is in the opposite direction from the magnetizing force.

Thus, if a vessel containing a weak aqueous solution of a paramagnetic salt of iron is suspended in a stronger solution of the same salt, and acted on by a magnet, the vessel moves as if it were magnetized in the opposite direction from that in which a magnet would set itself if suspended in the same place.

This may be explained by the hypothesis that the solution in the vessel is really magnetized in the same direction as the magnetic force, but that the solution which surrounds the vessel is magnetized more strongly in the same direction. Hence the vessel is like a weak magnet placed between two strong ones all mag-