## 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

We also found in (10-55) that it can be written solely in terms of the free charge

density for a linear isotropic homogeneous dielectric: V2</>=-^ (11-2) If the

relevant charge densities are zero, both of these reduce to

«> = 0 ...

We also found in (10-55) that it can be written solely in terms of the free charge

density for a linear isotropic homogeneous dielectric: V2</>=-^ (11-2) If the

relevant charge densities are zero, both of these reduce to

**Laplace's equation**V2«> = 0 ...

Page 172

We assume that, in addition to satisfying

points of the bounding surface S: <t> = const. on boundary (11-4) Now if we use (

1-115), (1-45), (1-17), and (11-3), we find that V • (<t> V</>) = V</> . V<//> + ...

We assume that, in addition to satisfying

**Laplace's equation**, <f> is constant on allpoints of the bounding surface S: <t> = const. on boundary (11-4) Now if we use (

1-115), (1-45), (1-17), and (11-3), we find that V • (<t> V</>) = V</> . V<//> + ...

Page 191

Upon comparing this with (11-92), we see that T, and P, satisfy the same

differential equation and thus 7} can be taken as, at most, ... Substituting this into (

11-96), we finally get the general form of the solution to

axially ...

Upon comparing this with (11-92), we see that T, and P, satisfy the same

differential equation and thus 7} can be taken as, at most, ... Substituting this into (

11-96), we finally get the general form of the solution to

**Laplace's equation**for anaxially ...

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angle assume axes axis becomes bound charge boundary conditions bounding surface calculate capacitance cavity charge density charge distribution charge q circuit conducting conductor const constant corresponding Coulomb's law current density curve cylinder dielectric dipole direction displacement distance divergence theorem electric field electromagnetic electrostatic energy equal equipotential evaluate example Exercise expression field point flux free charge function given illustrated in Figure induction infinitely long integral integrand Laplace's equation line charge located Lorentz transformation magnetic magnitude Maxwell's equations normal component obtained origin parallel plate capacitor particle perpendicular point charge polarized position vector potential difference quadrupole quantities rectangular coordinates region result satisfy scalar potential shown in Figure situation solenoid solution sphere of radius spherical surface charge surface charge density surface integral tangential components theorem total charge vacuum vector potential velocity volume write written xy plane zero