James Clerk Maxwell and Modern PhysicsGlazebrook, Richard
History
James Clerk Maxwell and Modern Physics
Glazebrook, Richard
Maxwell, James Clerk, 1831-1879; Physics -- History
When we are said to charge an insulated conductor we really act on the
ether in the neighbourhood of the body so as to store it with energy;
if there be another conductor in the field we cannot store energy in
the ether it contains. As, then, we pass from the outside of this
conductor to its interior there is a sudden change in some mechanical
quantity connected with the ether, and this change shows itself as a
force of attraction between the two conductors. Maxwell called the
change in structure, or in property, which occurs when a dielectric
is thus stored with electrostatic energy, _Electric Displacement_; if
we denote it by D, then the electric force R is equal to 4πD/K, and
hence the energy in a unit of volume is 2πD²/K, where K is a quantity
depending on the insulator.
Now, D, the electric displacement, is a quantity which has direction
as well as magnitude. Its value, therefore, at any point can be
represented by a straight line in the usual way; inside a conductor it
is zero. The total change in D, which takes place all over the surface
of a conductor as we enter it from the outside measures, according
to Maxwell, the total charge on the conductor. At points at which
the lines representing D enter the conductor the charge is negative;
at points at which they leave it the charge is positive; along the
lines of the displacement there exists throughout the ether a tension
measured by 2πD²/K; at right angles to these lines there is a pressure
of the same amount.
In addition to the above the components of the displacement D must
satisfy certain relations which can only be expressed in mathematical
form, the physical meaning of which it is difficult to state in
non-mathematical language.
When these relations are so expressed the problem of finding the value
of the displacement at all points of space becomes determinate, and
the forces acting on the conductors can be obtained. Moreover, the
total change of displacement on entering or leaving a conductor can be
calculated, and this gives the quantity which is known as the total
electrical charge on the conductor. The forces obtained by the above
method are exactly the same as those which would exist if we supposed
each conductor to be charged in the ordinary sense with the quantities
just found, and to attract or repel according to the ordinary laws.
If, then, we define electric displacement as that change which takes
place in a dielectric when it becomes the seat of electrostatic
energy, and if, further, we suppose that the change, whatever it
be mechanically, satisfies certain well-known laws, and that in
consequence certain pressures and tensions exist in the dielectric,
electrostatic problems can be solved without reference to a charge of
electricity residing on the conductors.
Public-domain text, read in full here on John Shaqi.
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