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Transcript
Electric Field ur ur F E= q Objectives 1. Properly explain/predict the behavior of objects, before and after being electrically charged/discharged. 2. Use equations and constants to solve word problems involving electric field, forces and motions of charged particles. Definition • • • • Electric Field is defined as Force per charge Units are Newtons per Coulomb (N/C) So, what’s an “Electric Field?” You have probably heard or even spoken of a “FORCE FIELD” – Esp in science fiction • You have been using equations to describe Gravity Fields already. • Let’s see how such “Force Fields” compare. Gravity vs. Electricity GMm F= 2 r æGM ÷ ö F = m çç 2 ÷ ÷ çè r ø F = g m q1q2 F = ke 2 r Qq F = ke 2 r F Q = ke 2 q r F = E q Gravity Field Electric Field Example 1 • A metal covered Styrofoam ball of mass 0.0050 kg and charged to 4.0 micro C is placed in an electric field and suspended motionless in midair. What is the strength of the electric field? Solution • Start with F=ma! • Free body diagram. Fe = qE Fg=mg • F = qE – mg = 0; • E=mg/q = 0.0050 x 9.8 / 4.0 x 10-6 =12000 N/C (12250 if you don’t like sig figs or units) ur ur F E= q Forces are vectors, so too must be the Electric Field. Sign - Arrows on field lines point away from positive charge. They show the direction of force by the field on a positively charged particle. Drawing! • Point charge +q Dipole • Electric dipole • Equal number of lines originate from pos charge and terminate at neg charge. • Note symmetry. Example 2 r q, m Q What is the acceleration of the small sphere? Conductors and Insulators • Conductors – charge (electrons) moves freely – (metals) • Insulators, …they don’t! (rubber, plastic, glass) • Field lines can help us determine where the charge on a conductor will reside. • Four rules… Rules for electrostatic equilibrium 1. Electric Field is zero everywhere INSIDE a conducting material. 2. Excess charge on a conductor resides entirely on its surface. 3. The electric field caused by a charged conductor is always perpendicular to its surface. 4. Charge is more concentrated at the smaller radius of irregularly shaped objects. Rules for electrostatic equilibrium Rule #1: Electric Field is zero everywhere INSIDE a conducting material. Reasoning: If there were an electric field inside a conductor, what would happen to the charge there? Rules for electrostatic equilibrium Rule #2: Excess charge on a conductor resides entirely on its surface. Reasoning: It’s complicated, but has to do with inverse square nature Coulomb’s Law. Think back to rule #1 Rules for electrostatic equilibrium Rule #3. The electric field caused by a charged conductor is always perpendicular to its surface. Reasoning: If it weren’t perpendicular, it would shove the charges sideways, not equilibrium. Rules for electrostatic equilibrium Rule #4. Charge is more concentrated at the smaller radius of irregularly shaped objects. Reasoning: Less sideways component of force. Van De Graaff • A number of the properties we’ve discussed can be demonstrated. • Like charges repel • Net Charge migrates to the outside • Field Lines perpendicular • “Dipole” How it works! Example 3 • A Van de Graaff dome of radius 0.20 meters is charged to 3.00 x 10-4 C. What is the strength and direction of the electric field at the following distances from the center? – 5.0 cm – 20.0 cm – 1.0 meter Picture 1.0 m 20.0 cm 5.0 cm Electric Field ur ur F Q E= = ke 2 q r For point charges The electric field may also be uniform, or approximated that way in many cases. This will simplify your math, just like little “g” simplifies things near the Earth’s surface. uur ur Fe = qE W = mg Millikan Oil drop experiment • Shows quantized nature of charge. (He got the Nobel Prize for this one.) + - Free Body Oil Drop Drag µ v falling qE rising -q -q Drag µ v mg mg http://chemistry.umeche.maine.edu/~amar/fall2004/Millikan.html Example 4 q m E What is the charge, Q, on the sphere? Faraday Ice Pail Experiment • Charge will migrate outward in conductors. • Touch a charged conductor to another just like it, ½ the charge will move to it. • But if you touch the inside of the neutral container, all of it will transfer! • Let’s draw to explain. AP note • Your equation sheet shows Coulomb’s Law as: 1 q1q2 F= 2 4pe0 r It also shows the value of e0 and ke. You can see they must be related. 1 ke = 4pe0 = 8.99 x109 (Nm 2 / C 2 ) e0 = 8.85 x10- 12 (C 2 / Nm 2 ) Wrap up 1. Properly explain/predict the behavior of objects, before and after being electrically charged/discharged. 2. Use equations and constants to solve word problems involving electric field, forces and motions of charged particles. Summary • Like charges repel, opposites attract • Charge is conserved, stripping one electron leaves a net charge of +e one beind and -e with the electron. • Net charge resides on surface • Concentrates at small radius • No field inside • Field lines perpendicular to surface • Point in direction a positive charge will be accelerated. • Charge is quantized at 1.6 x 10-19 C per elementary charge. • • Charge from one object will be shared with a neutral object if touched on the outside Charge will be completed given away when charged object is touched inside another Lightning Rods • What property of charged objects explains how they work? • page 493 #17, 18, 19, 20, 28, 34