This preview shows pages 1–10. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture 34 Applications of Gauss ’s Law ACT: Crossed planes Which diagram corresponds to the Efield lines for these two uniformly charged infinite sheets that intersect each other as shown? + σσ + σσ + σσ Each sheet produces a uniform electric field.σ + σ r t ot al E + r E r E The total E field is uniform in each quadrant. + σσ EXAMPLE: E for a charged sphere EXAMPLE: E for a charged sphere Find the magnitude of the electric field produced by a uniformly charged sphere with charge density ρ and radius R. First thing: Assess the symmetry of the problem. In this case, we clearly have a spherical symmetry. The magnitude of the electric field should only depend on the distance to the center of the sphere. Same E Direction of E : Must be radial (in for , out for +) If we want to find the electric field at a point located at distance r (>R) from the center of the sphere, the Gaussian surface to use is a sphere of radius r. r On the surface, the electric field and the differential area vector are parallel. r E (r) da Φ = = r r E da Eda Also, the electric field has the same magnitude all over the Gaussian surface: π = = 2 4 Eda E da E r 2 4 E r π Φ = Eqn. 1 The second way is using Gauss’s law. The charge enclosed by this surface is all the total charge in the sphere: 3 enclosed t ot al 4 3 q Q R ρ π = = So the flux through the Gaussian surface is also: 3 4 3 R ρ π ε Φ = Eqn. 2 Now we put everything together: 3 2 4 3 4 R E r ρ π π ε = It looks like the pointcharge electric field...
View
Full
Document
This note was uploaded on 03/27/2008 for the course PHYS 221 taught by Professor Herrerasiklody during the Fall '08 term at Iowa State.
 Fall '08
 HerreraSiklody
 Charge

Click to edit the document details