Physics 2102 Jonathan Dowling Flux Capacitor Schematic Physics

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Physics 2102 Jonathan Dowling Flux Capacitor (Schematic) Physics 2102 Lecture: 05 FRI 23 JAN

Physics 2102 Jonathan Dowling Flux Capacitor (Schematic) Physics 2102 Lecture: 05 FRI 23 JAN �Gauss’ Law I Version: 1/22/07 Carl Friedrich Gauss 1777 – 1855

What Are We Going to Learn? A Road Map • Electric charge - Electric

What Are We Going to Learn? A Road Map • Electric charge - Electric force on other electric charges - Electric field, and electric potential • Moving electric charges : current • Electronic circuit components: batteries, resistors, capacitors • Electric currents - Magnetic field - Magnetic force on moving charges • Time-varying magnetic field - Electric Field • More circuit components: inductors. • Electromagnetic waves - light waves • Geometrical Optics (light rays). • Physical optics (light waves)

What? — The Flux! STRONG E-Field Angle Matters Too Weak E-Field � d. A

What? — The Flux! STRONG E-Field Angle Matters Too Weak E-Field � d. A Number of E-Lines Through Differential Area “d. A” is a Measure of Strength

Electric Flux: Planar Surface • Given: – planar surface, area A – uniform field

Electric Flux: Planar Surface • Given: – planar surface, area A – uniform field E – E makes angle q with NORMAL to plane • Electric Flux: F = E • A = E A cosq • Units: Nm 2/C • Visualize: “Flow of Wind” Through “Window” E q normal AREA = A=An

Electric Flux: General Surface • For any general surface: break up into infinitesimal planar

Electric Flux: General Surface • For any general surface: break up into infinitesimal planar patches • Electric Flux F = E d. A • Surface integral • d. A is a vector normal to each patch and has a magnitude = |d. A|=d. A • CLOSED surfaces: – define the vector d. A as pointing OUTWARDS – Inward E gives negative flux F – Outward E gives positive flux F E d. A Area = d. A E d. A

Electric Flux: Example • Closed cylinder of length L, radius R • Uniform E

Electric Flux: Example • Closed cylinder of length L, radius R • Uniform E parallel to cylinder axis • What is the total electric flux through surface of cylinder? (a) (2 p. RL)E (b) 2(p. R 2)E (c) Zero (p. R 2)E–(p. R 2)E=0 What goes in — MUST come out! Hint! Surface area of sides of cylinder: 2 p. RL Surface area of top and bottom caps (each): p. R 2 d. A E L d. A R

Electric Flux: Example • Note that E is NORMAL to both bottom and top

Electric Flux: Example • Note that E is NORMAL to both bottom and top cap • E is PARALLEL to curved surface everywhere • So: F = F 1+ F 2 + F 3 = p. R 2 E + 0 – p. R 2 E = 0! • Physical interpretation: total “inflow” = total “outflow”! d. A 1 2 3 d. A

Electric Flux: Example • • Spherical surface of radius R=1 m; E is RADIALLY

Electric Flux: Example • • Spherical surface of radius R=1 m; E is RADIALLY INWARDS and has EQUAL magnitude of 10 N/C everywhere on surface What is the flux through the spherical surface? (a) (4/3)p. R 2 E = -13. 33 p Nm 2/C (b) 2 p. R 2 E = -20 p Nm 2/C (c) 4 p. R 2 E= -40 p Nm 2/C What could produce such a field? What is the flux if the sphere is not centered on the charge?

Electric Flux: Example r (Inward!) q (Outward!) Since r is Constant on the Sphere

Electric Flux: Example r (Inward!) q (Outward!) Since r is Constant on the Sphere — Remove E Outside the Integral! Surface Area Sphere Gauss’ Law: Special Case!