Electric Fields Review Coulombs Law Electric Fields Multiplecharge

Electric Fields • • Review Coulomb’s Law Electric Fields Multiple-charge Electric Fields Continuous-charge Electric Fields Parallel Plate Examples Gauss’s Law

Coulomb’s Law • • Fundamental property charge Positive and negative charge Units Coulombs (C) Force Law

Compare with gravitation • • Fundamental property mass Positive mass only Units kilograms (kg) Force Law

The “field” concept •

“Field” concept for gravity •

“Field” concept for electrostatic • Cellphone Tower – Multiple users sharing same tower. – Why calculate each tower/phone combination separately? • 2 step process – 1. Tower creates common “field”. – 2. Calculate each phone’s interaction with that “field”. • “Field” is # of “bars” you have! – Only difference is “field” varies more with r

Electrostatic vs. Gravitational Field •

Electric Field Animation • 2 -D animation https: //ef 55311 d-a-62 cb 3 a 1 a-ssites. googlegroups. com/site/physicsflash/Efield. swf? attachauth=ANo. Y 7 cr. Coduq. PW 1 yr. Sv. Mtvv 2 q. NVf. A 62 Nqyo. NF 1 X 8 FY 1 ldipscty_KXPmxm. My. KYNdrru. Nd 8 v. ROoq. OCxqee-i 4 Ld. S 8 Ct 27 v. Hf. Vi. Z 597 w 8 ETuqbnej. UPk. P 7 Ai. Kqr 4 M-S 3 qn 2 VLz. O 2 d. QNl_KXv. Re 0 j. Q 5 pu. GFnz. Kr. Pw. Zvuy 0 Uk. Mw. MU 4 Qh. Xh. JIIX 4 j. Wl. Ws. Qh. Qdgzqz-f 17 N 3 x. QOXv. Evfe. WC 1 O 3 Ob. HX 89 WV 72 w%3 D%3 D&attredirects=1

Electrostatic Field and Force Direction • - +

What if gravity was attractive/repulsive? ? ? • Positive and negative mass (!!) • (don’t worry, there isn’t such a thing) “Negative” mass falls to ceiling g “Positive” mass falls to floor

Electrostatic vs. Gravitational Field Electric Field Gravitational Field Can be anything Usually 9. 8 m/s 2 F=q 2 E F= m 2 g Force in field/opposite direction Force in field direction Field Definition Ratio of Force/charge Ratio of Force/mass, (simplifies to acceleration) Strength Electrostatic so strong appears on circuit-board scale Gravity so weak only appears on planetary scale Comment “E” quite interesting Varies all over the place “g” usually boring usually constant 9. 8 m/s 2 Can superimpose continuously Can superimpose discretely Wires, electrodes, circuit boards Planets, etc Field Concept Force & field Superposition

Electric Field - Example 16 -8 (1) •

Electric Field - Example 16 -8 (2) •

Electric Field - Example 16 -9 (1) • Get magnitudes

Electric Field - Example 16 -9 (2) • XY table Field X-component Y-component E 2 0 N/C +5 x 106 N/C E 1 +1. 1 x 106 N/C -0. 625 x 106 N/C Total +1. 1 x 106 N/C +4. 375 x 106 N/C

Continuous charge distributions • Coulomb’s Law plus a lot of integral calculus! (don’t worry, I’ll just show results) 1. Field of line of charge 2. Field of ring of charge 3. Field of sheet of charge 4. Field between 2 sheets of charge

1 - Field of Line of Charge

2 – Field of Ring of Charge

3 – Field of Sheet of Charge

Summary- Lines and Sheets of Charge

Summary- Continuous Charge Distributions •

4 – Field between 2 Sheets of Charge •

4 - Field between 2 Sheets of Charge •

Example - Photocopy Field •

Examples •

Examples •

Field Lines •

Gauss’s Law •

Gauss’s Law Examples 1. Point charge 2. Line of charge 3. Sheet of charge

Gauss’s Law 1 – Point charge •

Gauss’s Law 2 – Line charge •

Gauss’s Law 3 – Sheet charge •

Spring Break Assignment 1. Go skiing/Snowboarding 2. Take a spring mountain hike. 3. Walk around a hilly neighborhood. Slope electric field Elevation-> electric potential

Elevation vs Slope – Ski Map http: //www. skitaos. org/ Taos, NM

Elevation vs. Slope – contour lines Note contour lines If you know contour lines and spacing, you can calculate slope!!