7 04 
MR. G. F. C. SEARLE ON PROBLEMS IE ELECTRIC CONVECTION. 
Mechanical Force on a Charged Surface. 
18. The mechanical force experienced by any portion of a charged surface may be 
found by considering the difference of the Maxwell stress on the two sides of the 
surface. If the surface is an equilibrium surface, and if VQ is zero, there is neither 
electric nor magnetic force inside the surface, and consequently the Maxwell stress on 
the inner side vanishes. Let E and H be the electric and magnetic forces at a point 
just outside the surface. Then the Maxwell stress gives a normal outward force 
IvE 2 
87T 
(cos 3 6 — sin 3 6) — 
per unit area of the surface. Note that H lies in the tangent plane. 
There is also a tangential force in the plane containing E, u, and the normal, and it 
acts towards the E side of F ; its amount per unit of area is 
KF 3 
-— cos 6 sin 0. 
47 T 
The force experienced by the medium per unit volume is, by § 8, or by § 15, 
P = Ep + pVuB + 7- Y ^ B — YGD. 
4:77" dt 
The application of this formula to calculate the force experienced by the charged 
surface affords a good example of electromagnetic principles. We shall suppose that 
the electricity is uniformly distributed through a layer of small but finite thickness, a, 
Fig. 2. 
the volume-density being p, so that pa = o\ Now, if there is no disturbance on the 
side of the layer away from which it is moving, it follows that if E 0 and H 0 are the 
electric and magnetic forces at a point on the front of the layer, then the forces at any 
point 0 whose distance from the back of the layer is r, are 
E = — E 0 H = — K 0 . 
a u a 
