Electromagnetic FieldsThis revised edition provides patient guidance in its clear and organized presentation of problems. It is rich in variety, large in number and provides very careful treatment of relativity. One outstanding feature is the inclusion of simple, standard examples demonstrated in different methods that will allow students to enhance and understand their calculating abilities. There are over 145 worked examples; virtually all of the standard problems are included. |
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Page 171
... equation satisfied by . This is Poisson's equation , as given by ( 5-15 ) : - - ρ € 0 ( 11-1 ) where p is the total charge density . We also found in ( 10-55 ) that it can be written solely in terms of the free ... Laplace's Equation 11-2.
... equation satisfied by . This is Poisson's equation , as given by ( 5-15 ) : - - ρ € 0 ( 11-1 ) where p is the total charge density . We also found in ( 10-55 ) that it can be written solely in terms of the free ... Laplace's Equation 11-2.
Page 172
... Laplace's equation , & is constant on all points of the bounding surface S : $ = const . on boundary Now if we use ( 1-115 ) , ( 1-45 ) , ( 1-17 ) , and ( 11-3 ) , we find that ▽ · ( $ V $ ) = V4 · ▽ $ + $ ▽ 2 % = ( v ¢ ) 2 • which ...
... Laplace's equation , & is constant on all points of the bounding surface S : $ = const . on boundary Now if we use ( 1-115 ) , ( 1-45 ) , ( 1-17 ) , and ( 11-3 ) , we find that ▽ · ( $ V $ ) = V4 · ▽ $ + $ ▽ 2 % = ( v ¢ ) 2 • which ...
Page 191
... Laplace's equation and therefore = 1 / R , must be a solution of ( 11-87 ) . If we now substitute ( 11-94 ) into it , we obtain ∞ 1 dP Σ Gr " | 1 ( 1 + 1 ) P , + sino de ( sinod ) ] - 0 1 = 0 ( 11-95 ) In general , this sum can be zero ...
... Laplace's equation and therefore = 1 / R , must be a solution of ( 11-87 ) . If we now substitute ( 11-94 ) into it , we obtain ∞ 1 dP Σ Gr " | 1 ( 1 + 1 ) P , + sino de ( sinod ) ] - 0 1 = 0 ( 11-95 ) In general , this sum can be zero ...
Contents
INTRODUCTION | 1 |
ELECTRIC MULTIPOLES | 8 |
THE VECTOR POTENTIAL | 16 |
Copyright | |
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Ampère's law angle assume axes axis bound charge boundary conditions bounding surface calculate capacitance charge density charge distribution charge q circuit conductor consider const constant corresponding Coulomb's law curve cylinder dielectric dipole direction distance divergence theorem E₁ electric field electromagnetic electrostatic energy equation evaluate example expression field point free charge function given induction infinitely long integral integrand Laplace's equation line charge line integral located magnetic magnitude Maxwell's equations obtained origin P₁ perpendicular point charge polarized position vector potential difference quadrupole R₁ region result scalar potential Section shown in Figure sphere of radius spherical surface charge surface charge density surface integral tangential components theorem total charge vacuum vector potential velocity volume wave write written xy plane zero Απερ дх