Physics 2113 Jonathan Dowling Flux Capacitor Schematic Physics

Physics 2113 Jonathan Dowling Flux Capacitor (Schematic) Physics 2113 Lecture: 09 MON 15 SEP Gauss � Gauss’ Law I Carl Friedrich Gauss 1777 – 1855

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 θ d. A Number of E-Lines Through Differential Area “d. A” is a Measure of Strength

Electric Field & Force Law Depends on Geometry Point of Charge: Field Spreads in 3 D Like Inverse Area of Sphere = 1/(4πr 2) Line of Charge: Field Spreads in 2 D Like Inverse Circumference of Circle = 1/(2πr) Sheet of Charge: Field Spreads in 1 D Like A Constant — Does Not Spread!

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

Electric Flux: The General Case Air Flow Analogy

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

(a) EA? –EA? 0? (b) EA? –EA? 0? (c) EA? –EA? 0?

Electric Flux: ICPP • • 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)πR 3 E = -13. 33π Nm 3/C (b) 2πR E = -20π Nm/C (c) 4πR 2 E= -40π 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 — Remove E Outside the Integral! Surface Area Sphere Gauss’ Law: Special Case!

Gauss’s Law: Gravitational Field vs Electric Field r M r q