University:
Amherst College
Course:
PHYS 117 | Introductory Physics II: Electromagnetism and Optics
Academic year:

2020
Views:

235

Pages:

17
Author:

niewszytez7o

A parallel plate capacitor has two very large plates of area A separated by a small distance d. It is charged with equal charges of opposite sign. What is the magnitude of the electric field at point P, outside the capacitor? 1) Q 0 2) Q A 0 3) Q 2 A 0 Area A P d 4) Zero. Parallel-plate Capacitor • Electric Field for “infinite” sheet of charge: Area A d  E 2 0 James Clerk Maxwell (1831 – 1879) • Put electromagnetism on a solid theoretical footing. • Unified electromagnetism and optics by showing that light “is an electromagnetic disturbance propagated through the field.” (1864) • Devised a method to take the first color photographs. Figure 31.1 http://en.wikipedia.org/wiki/Color_photography Maxwell’s Equations – The Fundamental Laws of Electromagnetism • Gauss’ Law – The total electric flux through a closed surface is proportional to the charge enclosed:   Qencl ˆ EndA  0 • Gauss’ Law for Magnetism – The total magnetic flux through a closed surface is zero. – There are no magnetic charges.   Bnˆ dA  0 Maxwell’s Equations – The Fundamental Laws of Electromagnetism • Faraday’s Law – When the magnetic flux through some loop (C) changes, it induces an emf around the loop proportional to the rate of change of the magnetic flux.  dB d   N  N Bnˆ dA dt dt  Faraday’s Law • A changing magnetic field induces a curly electric field – one for which you cannot define a potential V.      d  Edl   Bnˆ dA dt  Figure 29.27c Maxwell’s Equations – The Fundamental Laws of Electromagnetism • Ampere’s Law (valid for constant currents)   – The integral of B  dl is proportional to the current piercing a surface bounded by the curve. – This Law needs generalization to the case of nonconstant currents.    Bdl 0 I encl  Figure 31.2   Bdl 0 I encl Figure 31.3 What is the total electric flux through Surface 1? 1) Q 0 2) Q A 0 3) 0 I 4) Zero. What is the total electric flux through Surface 2? 1) Q 0 2) Q A 0 3) 0 I 4) Zero. 5) Need more information. • Gauss’ Law – The total electric flux through a closed surface is proportional to the charge enclosed:   Qencl ˆ EndA  0 How is the current through Surface 1 related to the total electric flux through Surface 2? 1) I1   0  (ES 2) 2) d  (ES 2) I1   0 dt 3) Both are zero. 4) They are not related. 5) Need more information. What do the two surfaces have in common? • Surface S1: – Electric Flux = 0 so d  (ES 1) 0 0 dt – Current piercing the surface is I1. • Surface S2: d  (ES 2) 0 dt – Electric Flux is changing: – No current pierces surface. • For both surfaces the sum same. dE I  0 dt is the The Maxwell-Ampere Law   • The integral of B  dl around a closed curve is proportional to the current piercing a surface bounded by the curve plus  0 times the time rate of change of electric flux through the surface.    d    E Bdl 0  I encl   0  dt     d    ˆ Bdl 0  I encl   0 EndA  dt    Faraday’s Law   • The integral of E dl around a closed curve is proportional the time rate of change of magnetic flux through a surface that is bounded by the curve.    d  Edl   Bnˆ dA dt  Figure 29.27c

A Parallel Plate Capacitor

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