lecture5

# Palmer r august 8 2013 17 this

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: - Summer Session 2 - C. Palmer August 8, 2013 20 Charge Density +λ (C/m)   The electric field points away from the line of charge.   The normal to the surface also points in that direction. ˆˆ n=z ˆˆ n=r ˆ E (d ) r L Physics 2B - Summer Session 2 - C. Palmer August 8, 2013 d 21 Charge Density +λ (C/m)   Note that the direction of the electric field being purely in this direction is contingent on the line of charge being infinite in both directions. ˆˆ n=z ˆˆ n=r ˆ E (d ) r L Physics 2B - Summer Session 2 - C. Palmer August 8, 2013 d 22 Charge Density +λ (C/m)   Gauss’s Law ∫ QEnclosed E ⋅ dA = ε0 ˆˆ n=z ˆˆ n=r ˆ E (d ) r L Physics 2B - Summer Session 2 - C. Palmer August 8, 2013 d 23 Charge Density +λ (C/m)   Gauss’s Law (Lefthand Side) ∫ E ⋅ dA = ∫ ˆˆ E ( d ) r ⋅ r dA ∫ ˆˆ E ( r ) r ⋅ z dA Si de + Top + ∫ ˆˆ n=z ˆˆ n=r ˆ E (d ) r ˆˆ E ( r ) r ⋅ ( − zdA ) L d Bottom Physics 2B - Summer Session 2 - C. Palmer August 8, 2013 24 Charge Density +λ (C/m)   Gauss’s Law (Lefthand Side) ∫ E ⋅ dA = ∫ Si de ˆˆ E ( d ) r ⋅ r dA = E ( d ) 2π dL ˆˆ n=z ˆˆ n=r ˆ E (d ) r L Physics 2B - Summer Session 2 - C. Palmer August 8, 2013 d 25 Charge Density +λ (C/m)   Gauss’s Law (Righthand side) QEnclosed Lλ = ε0 ε0 ˆˆ n=z ˆˆ n=r ˆ E (d ) r L Physics 2B - Summer Session 2 - C. Palmer August 8, 2013 d 26 Charge Density +λ (C/m)   Gauss’s Law Lλ E ( d ) 2π dL = ε0 ˆˆ n=z ˆˆ n=r λ kE λ ⇒ E (d ) = =2 ˆ 2πε 0 d d E (d ) r L Physics 2B - Summer Session 2 - C. Palmer August 8, 2013 d 27   Gauss’s Law can be used to determine the electric field through OPEN surfaces when there is some symmetry to be exploited.   Often the open surface in question can be incorporated into a larger Gaussian surface.   Choosing the larger Gaussian surface is the tough part   Rule of thumb: Pick the surface where the electric field is constant.   Then the electric field comes out of the integral Physics 2B - Summer Session 2 - C. Palmer August 8, 2013 28   We have a point charge (+Q) at d/2 above the center an imaginary open surface which is square with side length d.   We would like to know the electric flux from the point charge’s field. Physics 2B - Summer Session 2 - C. Palmer August 8, 2013 29 ΦE = ∫ Surface d 2 E ⋅ dA = ∫ d − keQ ˆˆ z ⋅ r dx dy ∫−d 2 r 2 2 d 2   Doable… but hideous Physics 2B - Summer Session 2 - C. Palmer August 8, 2013 30   Imagine now that the square is one side of a cube and the charge lies at the center of it.   The geometry works because of the dimensions chosen.  ...
View Full Document

Ask a homework question - tutors are online