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SAT Electrostatics Electrostatics for AP Physics Alumni I separated the electrostatics from the rest of the electricity and magnetism stuff because it is the most closely related to mechanics. You can understand most of it by adapting what you already know about potential and kinetic energy, work, and universal gravitation. The Analogy Electrical energy is a lot like gravitational potential energy. Gravitational Electrical objects can move charges can move objects can have potential energy charges can have potential energy potential energy can become motion potential energy can become motion the quality of the object that affects how the quality of the object that affects how much much potential energy it has is its MASS potential energy it has is its CHARGE mass is a positive scalar that’s always charge is a scalar that can be positive or conserved negative and it’s always conserved the aspect of the position of the object the aspect of the position of the object that that affects how much potential energy affects how much potential energy it has is its it has is its HEIGHT ELECTRICAL POTENTIAL aka VOLTAGE Higher objects have potential energy Higher-potential objects have potential because of gravitational attraction energy because of electrostatic attraction and/or repulsion The equation about gravitational force is The equation about electrostatic force is Gm m kq q F = 1 2 F = 1 2 g d 2 e d 2 The gravitational force is only attractive. The electrostatic force can be attractive or repulsive. Work done against the gravitational Work done against the electrostatic force force makes an equal amount of makes an equal amount of electrostatic gravitational potential energy. potential energy. Charges and Forces (Hewitt 32.3) You probably learned this in middle school: there are positive and negative charges – like charges repel and opposite charges attract. The equation is Coulomb’s law: kq q F = 1 2 e d 2 Fe = electrostatic force (N) k = Coulomb constant = 9.0 ×109 N ⋅m2 / C2 q1,q2 = charges (C) d = distance between charges (m) The unit of charge is the Coulomb (C). It’s a really big unit, so you usually see something like µC (microCoulombs) in the problems. The direction of the force is along the line that connects the two objects, toward the other object if they’re opposite charges and away from it if they’re the same charge. You can put this force in a free-body diagram! Notice how much Coulomb’s law looks like Newton’s Law of Universal Gravitation. They’re both inverse-square laws so the amount of force decreases rapidly as you move away from the other object, like this: The Nature of Charge (Hewitt 32.1-32.2) You know from chemistry and stuff that electrons are negatively charged and protons are positively charged. An object is “charged” if it has a different total number of protons and electrons. If there are more electrons, it is negative, if there are more protons, it is positive. An object can become charged by having electrons added to or subtracted from it. One easy way to do this is to rub the object against another object. If the two types of material are different, electrons will go from one to the other, causing one to become positively charged and the other negatively charged. Because the charge has to do with the total number of electrons and electrons don’t just appear and disappear, the total amount of charge in an interaction is always conserved. When a charged object touches another object, the amount of charge is shared between the objects, it averages out. For example, if an object with a charge of + 6.0 µC touches an object with a charge of -4.0 µC, then together they’ll have + 2.0 µC and when you separate them, they’ll each have + 1.0 µC. Makes sense, right? Electric Fields (Hewitt 33.1-33.2) In physics, a field is a region of space in which some objects feel a force. When you have weight and feel the force of gravity, you are in a gravitational field. When charged particles feel a force, they are in an electric field. Part of the reason for the magnitude of the force is the amount of charge the object has and the rest of the reason is because of the field. We call this the electrical field strength, and it is simply the force felt by a particle divided by the particle’s charge: F E = q E = electrical field strength (N/C) F = Force (N) q = charge (C) Electric fields can be uniform (the same strength everywhere) or non-uniform (stronger in some parts than others. The field near a charged object is non-uniform because the closer you get to the charged object, the more force you feel. They like to talk about hollow conducting spheres. What happens inside the sphere is analogous to gravity inside a planet. The field decreases from what it is at the surface to zero linearly (whereas it decreases as an inverse square on the outside). We depict electric fields with electric field lines. The are always drawn in the direction that a positive test charge would feel a force, so they go from plus to minus. When the field lines are closer together, the field is stronger. Work and Potential Energy (Hewitt 33.4) kq q Coulomb’s Law F = 1 2 tells us the force that a charge feels near another charge. We e d 2 know that potential energy is equal to the work it takes to get a charge to a that place from a place where it had no potential energy. The calculation is really similar to the calculation we did to find the potential energy of an object in space near another object. kq q U = 1 2 d U = potential energy (J) k = Coulomb constant = 9.0 ×109 N ⋅m2 / C2 q1,q2 = charges (C) d = distance between charges (m) Electric Potential (Hewitt 33.5) It is convenient to separate the contribution to the electrical potential energy from the charge to the contribution from the environment (from the electric field). This is analogous to saying that a boulder on a cliff has potential energy for two reason: its mass and the height of the cliff. The electric potential is the height of the cliff. To find it, we just divide the electrical potential energy by the charge. U V = q V = electric potential (V) U = potential energy (J) q = charge (C) .
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