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07. 07. 20031 PY212 Electricity and Magnetism I. Electrostatics

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07. 07. 20032 I-1 Electric Charge

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07. 07. 20033 Main Topics Why Electrostatics? Demonstration of Electrostatic Effects. Electric Charge and its Properties. Coulomb’s Law. Some Applications of the C. L. Electric Field and Electric Intensity

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07. 07. 20034 Why Electrostatics? Many important properties of the Nature exist due to electric interactions of charged particles. We shall first deal with fields and charges which are static = do not move. It is for simplicity but such fields really exist, if some equilibrium can be reached!

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07. 07. 20035 Demonstration of Electrostatic Effects A comb after it has been run through hair attracts little pieces of paper. The force is a long-distance one. It can be attractive or repulsive. We attribute these forces to the existence of a property we call the electric charge. Bodies can be charged by conduction via contact with other bodies but even remotely by induction. Using some materials we can easily discharge charged bodies, these are conductors. By others it is slow or even impossible, they are insulators

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07. 07. 20036 Main Properties of Charges Since both the attractive and the repulsive forces exist, charges must be of two kinds, positive and negative. Unlike charges attract and like charges repel themselves. Charges are quantized. They can only be isolated in integer multiples of the elementary charge e = 1.602 10 -19 C In all known processes charges appear or disappear only in pairs (+q and -q), so the total charge is conserved Charge is invariant to the Lorentz transformation

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07. 07. 20037 Main Properties of Electrostatic Interactions Charged particles act by a force on each other. Forces : are Long-distance – mediated by electric field obey the principle of superposition Mutual interaction of two static point charges is described by Coulomb’s Law

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07. 07. 20038 Coulomb’s Law I Let us have two point charges Q 1 and Q 2 at the distance r apart. Then the magnitude of the interaction force is:magnitude F = k Q 1 Q 2 / r 2 The SI unit of charge is 1 Coulomb [1 C] k = 9 10 9 Nm 2 /C 2 k = 1/4 0 0 = 8.85 10 -12 C 2 / Nm 2 is the permitivity of vacuum

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07. 07. 20039 Coulom’s Law II Since forces are involved the directional information is as important as the magnitude. To get the full information let’s place Q 1 into the origin and let describe the position of Q 2 by the radius vector. Then the force acting on Q 2 is : Forces act in the straight line joining the charges. Positive force is repulsive. Forces acting on Q 1 and Q 2 are action and reaction of each other.

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07. 07. 200310 Coulomb’s Law III The most general formula we get if we define the position of each charge Q i (i=1, 2) by its own radius vector. Then the force acting on Q 2 is : Since the force depends only on the difference between the radius vectors, the position of the origin is arbitrary.

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07. 07. 200311 Comparison with the Force of Gravity Formally, Coulomb’s Law is Analogous to Newton’s Gravitational Law But electrostatic force is ~ 10 42 (!) times stronger stronger Such a weak force still dominates the universe because matter is usually neutralneutral Charging something means to break very slightly the great equilibriumgreat

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07. 07. 200312 The Concept of the Field If a charge is located in some point in the space it sends around an information about its position, polarity and magnitude. The information spreads with the speed of light. It can be “received” by another charge. The interaction of a charge with field produces a force.

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07. 07. 200313 Electric Intensity I Electrostatic field could be described by taking some test charge Q and recording the vector of the force acting on it in every point of interest. This description would, however, depend on the magnitude and polarity of the test charge and these properties would have to be provided as the additional information to make the description unique.

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07. 07. 200314 Electric Intensity II By dividing of the force by the magnitude of the test charge the electric intensity is defined : It is a unique property of the described field, now. Numerically it is equal to the force which would act in the particular point on a unit positive charge, but be careful with dimensions.

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07. 07. 200315 Electric Intensity III It is important to realize that by dividing by the magnitude of the charge, the information, how the charge ‘feels’ the field, becomes an objective property of the field. The same field acts on various charges by various forces which can be even opposite due to the existence of two polarities of charges.

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07. 07. 200316 Electric Field Lines I Electric field is a three dimensional vector field which is in general case difficult to visualize. In cases of simple symmetry, it is possible to use electric field lines which are lines tangent to vectors of the electric intensity in every point. The magnitude of the field can be illustrated by their length or density.

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07. 07. 200317 Electric Field Lines II A positive charge of a very little mass would move along a certain field line in the direction of the electric field while negative charge would move in the opposite direction. Field lines can’t cross!

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07. 07. 200318 Homework 1 The homework is selected from “problem” sections that are in the end of each chapter. Due Wednesday ! 21- 2, 7, 9, 14, 15

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07. 07. 200319 Things to Read : This lecture covers: Giancoli: Chapter 21, Sections 1-8 (ex. 7) Advance reading : Giancoli:Chapter 22

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Two electrons 1 m apart They are repelled by electric force but attracted by the force of gravitation. Which force will prevail? ^

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One electron and one proton 0.53 10 -10 m apart This corresponds to their distance in hydrogen atom. Force of this magnitude can be in principle measured macroscopically! This is the secret why matter holds together. ^

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Let us separate protons and electrons from one gram of H and put each group on each pole of the Earth 1 g is 1 gram-molecule of H, so we have N A =6.02 10 23 of both types of particles. ^

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Two 1g iron spheres, 1 m apart are attracted by the force of 10 N. What is their excess charge compared to the total charge? The excess charge: The total charge: ^

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