Introduction to Electromagnetism - 5

Announcements Define Flux Electric field lines passing through a surface Define Gaussian Surface A closed surface Can be imaginary (that is, does not have to coincide with any real surface) Look for symmetry Geometrical symmetry should simplify the calculations. Field Due to a Spherically Symmetric Charge Distribution Spherically Symmetric, cont. Spherically Symmetric Distribution, final Field Due to a Thin Spherical Shell Use spheres as the gaussian surfaces When r a, the charge inside the surface is Q and E keQ / r2 When r a, the charge inside the surface is 0 and E 0 Coulomb vs. Gauss A comparison Field at a Distance from a Line of Charge (Gauss) Field Due to a Line of Charge, cont. The end view confirms the field is perpendicular to the curved surface The field through the ends of the cylinder is 0 since the field is parallel to these surfaces Field Due to a Line of Charge, final Field Due to a Plane of Charge E must be perpendicular to the plane and must have the same magnitude at all points equidistant from the plane Choose a small cylinder whose axis is perpendicular to the plane for the gaussian surface Field Due to a Plane of Charge, cont E is parallel to the curved surface and there is no contribution to the surface area from this curved part of the cylinder The flux through each end of the cylinder is EA and so the total flux is 2EA Field Due to a Plane of Charge, final Click to edit Master title style Click to edit Master text styles Second level Third level Fourth level Fifth level Instructor Franco Gaspari PHY 1040U (Physics for the biosciences) Introduction to Electromagnetism and Optics Lecture 5 January 23, 2007 dy Problem calculate By symmetry, we can consider of the rod and multiply by 2. Symmetry also tells us that we consider only the x component. dy Multiply x2 g ) L