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Lecture 1 agenda: Electric Charge. Just a reminder of some things you learned back in grade school. Coulomb’s Law (electrical force between charged particles). You must be able to calculate the electrical forces between one or more charged particles. The electric field. You must be able to calculate the force on a charged particle in an electric field. Electric field due to point charges. You must be able to calculate electric field of one or more point charges. Motion of a charged particle in a uniform electric field. You must be able to solve for the trajectory of a charged particle in a uniform electric field. Coulomb’s Law: it’s just part of a bigger picture Coulomb's Law quantifies the interaction between charged particles. 1 F = 12 4πε 0 q 1q 2 2 12 r r12 , + - Q1 Q2 Charged particles exert forces on each other over great distances. How does a charged particle "know" another one is “there?” We use the concept of an electric field to explain this interaction. Here's the idea… The Electric Field F12 A charged particle propagates (sends out) a "field" into all space. Other charged particles sense the field, and “know” that the first one is there. + + like charges repel A charged particle modifies the properties of the space around it. F21 F13 F31 unlike charges attract The idea of an electric field is good for a number of reasons: It makes us feel good, like we’ve actually explained something. OK, that was a flippant remark. There are serious reasons why the idea is “good.” We can develop a theory based on this idea. From this theory may spring unimagined inventions. If the theory explains past observations and leads to new predictions, the idea was “good.” The electric field is real! F12 + F13 F31 + F21 like charges repel unlike charges attract Trust me. Or go stand outside in an electric storm and then try to tell me the electric field is not real. Some physicists will tell you the electric field is real. Others disagree. It seems to depend on what you define “real” to mean. We define the electric field by the force it exerts on a test charge q0: E = F0 The subscript “0” reminds you the force is on the “test charge.” I won’t require the subscripts when you use this equation for boardwork or on exams. q0 If the test charge is "too big" it perturbs the electric field, so the “correct” definition is E = lim q0 0 F0 q0 You won’t be required to use this version of the equation. Any time you know the electric field, you can use this equation to calculate the force on a charged particle in that electric field: F = qE This version of the electric field equation is on your equation sheet. Use it for problems involving electric fields and forces: I’m not mad, I tell you, not mad. The little voices tell me I’m quite sane. F = qE This is your second starting equation. The equation tells you the direction of the electric field is the direction of the force exerted on a POSITIVE test charge. The absence of absolute value signs around q means you MUST include the sign of q in your work. F0 N E = = q 0 C The units of electric field are newtons/coulomb. In chapter 3, you will learn that the units of electric field can also be expressed as volts/meter: E = N C = V m The electric field can exist independent of whether there is a charged particle around to “feel” it. Remember: the electric field direction is the direction a + charge would feel a force. + A + charge would be repelled by another + charge. Therefore the direction of the electric field is away from positive (and towards negative). http://regentsprep.org/Regents/physics/phys03/afieldint/default.htm Gravitational Fields The idea of a field is not new to you. You experienced fields (gravitational) in Physics 1135. FG =G g( r) = m 1m 2 2 12 , attractive r FG m Units of g are actually N/kg! g( r) is the local gravitational field. On earth, it is about 9.8 N/kg, directed towards the center of the earth. A particle with mass modifies the properties of the space around it. If the last equation looks like this, you have missing fonts. Lecture 1 agenda: Electric Charge. Just a reminder of some things you learned back in grade school. Coulomb’s Law (electrical force between charged particles). You must be able to calculate the electrical forces between one or more charged particles. The electric field. You must be able to calculate the force on a charged particle in an electric field. Electric field due to point charges. You must be able to calculate electric field of one or more point charges. Motion of a charged particle in a uniform electric field. You must be able to solve for the trajectory of a charged particle in a uniform electric field. The Electric Field Due to a Point Charge Coulomb's law says F =k 12 q 1q 2 2 12 , r ... which tells us the electric field due to a point charge q is E q =k q r 2 , aw ay from + …or just… E=k q r This is your third starting equation. 2 E=k q r 2 A physics 2135 equation is like a toaster! You wouldn’t shove yogurt down your toaster, would you? You can’t expect to just shove numbers into an equation and out pops the correct answer. To experience the optimum user satisfaction from your physics 2135 toaster equations you need to understand what they mean and think about what you are doing with them. If we define rˆ as a unit vector from the source point to the field point… source point rˆ + field point …then the equation for the electric field of a point charge becomes: E =k q r 2 rˆ Consult a professional before using. Do not use more than 4 times a day without seeing your physicist. May cause headaches, dizziness, and upset stomach. Drink a full glass of water with each use. You may start with either equation for the electric field (this one or the one on the previous slide). But don’t use this one unless you REALLY know what you are doing! (So for now don’t use it!)