Physics 102 Chapter 23-24 notes

Physics 102 Chapter 23-24 notes - Coulombs Law You are...

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Coulomb’s Law You are expected to: A) Use Coulomb’s law to calculate the electric forces between charges. B) Calculate the E -field due to a discrete charge distribution and simple continuous charge distributions. C) Know the distinction between the electric force F (see eqs. [1], [2] below) and the E -field. D) Use Gauss’ law to calculate the E -field for symmetric continuous charge distributions. E) Solve problems that contain concepts from this chapter + some simple concepts from PHYS-101. 1 Coulomb’s Law According to Coulomb’s Law, the magnitude of the electrostatic force between two charged particles with charges Q 1 and Q 2 and separated by a distance r is given by: F e = k e Q 1 Q 2 r 2 , (1) where k e = 9x10 9 N · m 2 /C 2 is the Coulomb constant. The unit of charge is taken as a Coulomb (C). The constant k e is also written as k e = 1/4πε o where the constant ε o is called the permittivity of free space ε o = 8.854x10 -12 C 2 / N · m 2 . Since force is a vector quantity, in the vector form Coulomb’s law is expressed as: F 12 = k e Q 1 Q 2 r 2 r 12 (2) where r 12 is a unit vector directed from Q 1 to Q 2 . The electric charge is quantized in units of 1.6 10 - 19 C (magnitude of the charge of an electron).
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Problem Solving: 1.1 Finding force on a given charge due to a discrete charge distribution. Break up the problem in three parts: [1] Direction : draw the force vectors at a given charge location due to the other given charges (Remember: like charges repel, unlike charges attract). A well-labeled diagram will be very helpful. [2] Magnitude : find the magnitude of various force vectors using eq. [1]. [3] after step [2] treat the problem as a vector manipulation problem. The net force F on a given charge due to a discrete charge distribution is simply the vector sum of the forces produced by individual charges in the charge distribution at the location of the charge of your interest. Study problem 2 below to clarify the points mentioned above. 2 The E-field The magnitude of the E -field generated by a charge Q is given by E = kQ/r 2 . The direction of E at a given location is the direction in which a force would be exerted on a unit positive test charge placed at that location. The E -field due to a discrete charge distribution is simply the vector sum of the E -fields produced by individual charges in the charge distribution. 2.1 Finding the E-field at a given location due to a discrete charge distribution.
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This note was uploaded on 11/11/2011 for the course ENGR 231 taught by Professor Olehtretiak during the Fall '10 term at Drexel.

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Physics 102 Chapter 23-24 notes - Coulombs Law You are...

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