Listrik Magnet (4)

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Listrik Magnet Umiatin, M.Si Sesion #04 JurusanFisika FakultasMatematikadanIlmuPengetahuanAlam © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 1 1/7/2011

Outline DeskripsiPotensialListrik Persamaan Poisson dan Laplace PotensialdariDistribusiMuatanTerlokalisasi 1/7/2011 © 2010 UniversitasNegeri Jakarta | www.unj.ac.id | 2

ELECTROSTATICS 1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 3

1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 4

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1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 19 Separation Variable Method When the potential or charge distribution is specified on the boundaries on some region and we want to find the potential in the interior, the best strategy is solving Laplace’s equation directly through separation variable method. By analyzing the problem we can choose appropriate coordinate system.

1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 20 Example 1 : Two infinite metal grounded lie parallel to the xz plane, one at y = o, the other at y = a. The left end, at x = 0, is closed of with infinite strip insulated from the two plates and maintained at a specific potential Vo(y). Find the potential inside the slot !

1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 21 Solution : Illustrate the problem in to cartesian coordinate system. Its two dimensional problem.

1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 22 Laplace’ eq : By subtituting the solution below into Laplace’s eq We get

1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 23 Using boundary condition iv:

1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 24 Condition i D = 0 Condition ii sin ka = 0

1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 25 Next, determine the coefficients Cn

1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 26

1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 27

Thank You 1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 28

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Listrik Magnet (4)

19. 1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 19 Separation Variable Method When the potential or charge distribution is specified on the boundaries on some region and we want to find the potential in the interior, the best strategy is solving Laplace’s equation directly through separation variable method. By analyzing the problem we can choose appropriate coordinate system.

20. 1/7/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 20 Example 1 : Two infinite metal grounded lie parallel to the xz plane, one at y = o, the other at y = a. The left end, at x = 0, is closed of with infinite strip insulated from the two plates and maintained at a specific potential Vo(y). Find the potential inside the slot !