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Unformatted text preview: 1 1 Swartz 06/5/13 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 3: ECE 3030 Electromagnetic Fields and Waves Instructor: Dr. Wesley E. Swartz Fall 2008 Lecture 3 2008/9/3 Electrostatics Application of Gauss’ Law Superposition Principle Fields of Some Charge Distributions q + q − x E A 2 Swartz 06/5/13 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 3: Announcements • We will not be able to “move” any of the Demo or Workshop sections to accommodate conflicts. • If you have only a conflict for the Demo sections – there is something blowing in the wind that might help. – However, if your conflict results from trying to take ENGRD 2300, ECE 3100, and ECE 3030, then • You should realize you are taking on a huge burden… – All three of these courses are major undertakings! • I recommend you have a talk with your advisor! • If you have only a conflict for the Workshop sections, then – You 3 Swartz 06/5/13 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 3: Simple Charge Distributions • A single charge • A Charged plate • A ring of charge • A line charge • Oppositely charged plates • Dipoles – a pair of opposite charges 4 Swartz 06/5/13 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 3: Field of a Point Charge • Consider a point charge of q Coulombs sitting at • Surround the charge by a Gaussian surface in the form of a spherical shell of radius r – By symmetry , the Efield magnitude on the surface must be uniform and pointing in the radial direction = r q Using Gauss’ Law: ( ) q r E r o = 2 4 π ε r r q E r q E o o r ˆ 4 or 4 2 2 πε πε = = r q 5 Swartz 06/5/13 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 3: Field of an Infinite Charged Plane • Suppose we have a charged plane. – Let the surface charge density be • Coulombs/m2 – Symmetry Argument: The charge distribution is symmetric w.r.t. +z and –z directions. • Therefore, if at any point there is an Efield component in the + z direction, there must also be Efield component in the – z direction. • Since the field cannot have a zcomponent pointing in both + z and – z directions at the same time, there cannot be a zcomponent of the field. • Similarly, there cannot be a ycomponent of the Efield • So the field can only have an xcomponent x z y 6 Swartz 06/5/13 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 3: Field of an Infinite Charged Plane • Since the field can only have an xcomponent, – Draw a Gaussian surface in the form of a cylinder of area A piercing the charged plane – Total flux coming out of the cylinder ends = – Total charge enclosed by the surface = – By Gauss’ Law: x z y A E x o ε 2 A o x x o E A A E ε ε 2 2 = = x E A 2 7 Swartz 06/5/13 ECE 303 – Electromagnetic Fields and Waves – Fall 2008 Lecture 3: Boundary Conditions for Surface Charges...
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This note was uploaded on 10/15/2008 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell.
 Fall '06
 RANA
 Electromagnet

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