## Classical Electrodynamics |

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Page 45

36 ) n = 1 the define then we can ask for the best choice of

we get the " best " representation of the function ( 9 ) . If " best " is defined as

minimizing the mean square error My : My – L \ 50 – 3 a , U _ c8 ) * a ( 2 . 37 ) n =

1 it ...

36 ) n = 1 the define then we can ask for the best choice of

**coefficients**a , so thatwe get the " best " representation of the function ( 9 ) . If " best " is defined as

minimizing the mean square error My : My – L \ 50 – 3 a , U _ c8 ) * a ( 2 . 37 ) n =

1 it ...

Page 61

34 ) This is just a Legendre series of the form ( 3 . 23 ) , so that the

are : P2 ( cos O ) sin 0 do ( 3 . 35 ) 2a ' JO A - 21 + 1 If , for example , V ( O ) is that

of Section 2 . 8 , with two hemispheres at equal and opposite potentials , .

34 ) This is just a Legendre series of the form ( 3 . 23 ) , so that the

**coefficients**A ,are : P2 ( cos O ) sin 0 do ( 3 . 35 ) 2a ' JO A - 21 + 1 If , for example , V ( O ) is that

of Section 2 . 8 , with two hemispheres at equal and opposite potentials , .

Page 544

The

condition V . B = 0 must be satisfied . Since the radial functions are linearly

independent , the condition V . B = 0 must hold for the two sets of terms in ( 16 .

The

**coefficients**Aim in ( 16 . 35 ) are not completely arbitrary . The divergencecondition V . B = 0 must be satisfied . Since the radial functions are linearly

independent , the condition V . B = 0 must hold for the two sets of terms in ( 16 .

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### Contents

Introduction to Electrostatics | 1 |

References and suggested reading | 50 |

Multipoles Electrostatics of Macroscopic Media | 98 |

Copyright | |

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acceleration angle angular applied approximation assumed atomic average axis becomes boundary conditions calculate called Chapter charge charged particle classical coefficients collisions compared component conducting Consequently consider constant coordinates cross section cylinder defined density dependence derivative determine dielectric dimensions dipole direction discussed distance distribution effects electric field electromagnetic electron electrostatic energy equal equation example expansion expression factor force frame frequency function given gives incident inside integral involved light limit Lorentz loss magnetic magnetic field magnetic induction magnitude mass means momentum motion moving multipole normal observation obtain origin parallel particle physical plane plasma polarization position potential problem properties radiation radius region relation relative relativistic result satisfy scalar scattering shown in Fig shows side solution space sphere spherical surface transformation unit vanishes vector velocity volume wave written