By K. J. Binns
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The normal component of field due to the equivalent surface charge distribution is then, from eqn. 16) FIG. 17) Hence eqn. 18) and this gives the normal component of field strength along the perimeter of the circle due to the distributed charge. But this is the normal component of field due to a charge —q(£2—£i)/(£2-f-£i) at inverse point B together with a charge + q(s —ei)/(e +ei) at the centre of the circle. Therefore, since these charges are inside the boundary they are the required image charges which, together with the applied charge, give the field outside the circular boundary.
J. LODGE, On some problems connected with the flow of electricity in a plane, Phil. , 5th series, 1, 373-89 and 2 , 37-47 (1876). 2. G . F. C. SEARLE, On the magnetic field due to a current in a wire placed parallel to the axis of a cylinder of iron, The Electrician 453 and 510 (1898). 3. P. HAMMOND, Electric and magnetic images, Proc. Instn. Elect. Engrs. 107 C, 306 (1960). 4. N . MULLINEUX and J. R. REED, Images of line charges and currents, Proc. Instn. Elect. Engrs. I l l , 1343. 5. F. CHORLTON, Circle and sphere theorems in potential theory and the determination of image systems, Birm.
The idea of images for field problems is due to Lord Kelvin, but Maxwell, Lodge, and Searle extended the scope of the method. The essence of the method consists in replacing the effects of a boundary on an applied field by simple distributions of currents or charges behind the boundary line (called images), the desired field being given by the sum of the applied and the image fields. A different system of images is required for the field on each side of a boundary, but a knowledge of one group of images quickly leads to the other, since the solutions for the two regions are connected by the boundary conditions.
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