Light Pressure

The doctrines peculiar to Maxwell are the existence of:

• displacement-currents, and
• electromagnetic vibrations identical with light

Faraday [62] studied the curvature of lines of force in electrostatic fields. He had noticed a tendency of adjacent lines to repel each other, as if each tube of force were inherently disposed to distend laterally.

In addition to this repellent or diverging force in the transverse direction, he supposed an attractive or contractile force to be exerted at right angles to it in the direction of the lines of force.

Maxwell was fully persuaded of the existence of these pressures and tensions.

• He created analytical expressions suitable to represent them.

The tension along the lines of force must be supposed to maintain the ponderomotive force which acts on the conductor on which the lines of force terminate.

It may therefore be measured by the force which is exerted on unit area of the conductor, i.e., εE2/8πc2 or DE.

The pressure at right angles to the lines of force must then be determined so as to satisfy the condition that the aether is to be in equilibrium.

Consider a thin shell of aether included between two equipotential surfaces.

The equilibrium of the portion of this shell which is intercepted by a tube of force: requires (as in the theory of the equilibrium of liquid films), that the resultant force per unit area due to the abovementioned normal tensions on its two faces shall have the value T(1/ρ1 + 1/ρ2), where ρ1 and ρ2 denote the principal radii of curvature of the shell at the place.

Where T denotes. the lateral stress across unit length of the surface of the shell, I being analogous to the surface-tension of a liquid film.

If t denotes the thickness of the shell, the area intercepted on the second face by the tube of force bears to the area intercepted on the first face the ratio (ρ1 + t) (ρ2 + t)/ρ1ρ2; and by the fundamental property of tubes of force, D and E vary inversely as the cross-section of the tube, so the total force on the second face will bear to that on the first face the ratio

ρ1ρ2/(ρ1 + t) (ρ2 + t),

or approximately

(1 - t/ρ1 - tρ2);

the resultant force per unit area along the outward normal is

…

therefore

…

and so we have

…

or the pressure at right angles to the lines of force is

…

DE per unit area—that is, it is numerically equal to the tension along the lines of force.

The principal stresses in the medium being thus determined, it readily follows that the stress across any plane, to which the unit vector N is normal, is

…

Maxwell obtained[63] a similar formula for the case of magnetic fields.

The pouderomotive forces on magnetized matter and on conductors carrying currents may be accounted for by assuming a stress in the medium, the stress across the plane N being represented by the vector

…

This, like the corresponding electrostatic formula, represents a tension across planes perpendicular to the lines of force, and a pressure across planes parallel to them.

Maxwell made no distinction between stress in the material dielectric and stress in the aether. As long as material bodies when displaced carry the contained aether along with them, then no distinction was possible.

Maxwell’s theory was modified many years afterwards by his followers.

Stresses corresponding to those introduced by Maxwell were assigned to the aether, as distinct from ponderable matter. It was assumed that the only stresses set up in material bodies by the electromagnetic field are produced indirectly.

They may be calculated by the methods of the theory of elasticity, from & knowledge of the ponderomotive forces exerted on the electric charges connected with the bodies.

Maxwell’s theory considered the question of stress in the medium from the purely statical point of view.

He determined the stress so that it might produce the required forces on ponderable bodies, and be self-equilibrating in free aether.

But[64] if the electric and magnetic phenomena are really kinetic in their nature and not static, then the stress or pressure need not be self-equilibrating.

This is illustrated by reference to the hydrodynamical models of the aether in which perforated solids are immersed in a moving liquid.

The ponderomotive forces exerted on the solids by the liquid correspond to those which act on conductors carrying currents in a magnetic field, and yet there is no stress in the medium beyond the pressure of the liquid.