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Ch0203

# Ch0203 - Chapter 3 The Electric Field Due to one or more...

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Chapter 3 The Electric Field Due to one or more Point Charges 14 3 The Electric Field Due to one or more Point Charges A charged particle (a.k.a. a point charge, a.k.a. a source charge) causes an electric field to exist in the region of space around itself. This is Coulomb’s Law for the Electric Field in conceptual form. The region of space around a charged particle is actually the rest of the universe. In practice, the electric field at points in space that are far from the source charge is negligible because the electric field due to a point charge “dies off like one over r-squared.” In other words, the electric field due to a point charge obeys an inverse square law, which means, that the electric field due to a point charge is proportional to the reciprocal of the square of the distance that the point in space, at which we wish to know the electric field, is from the point charge that is causing the electric field to exist. In equation form, Coulomb’s Law for the magnitude of the electric field due to a point charge reads 2 r q k E = (3-1) where E is the magnitude of the electric field at a point in space, k is the universal Coulomb constant 2 2 9 C m N 10 99 8 × = . k , q is the charge of the particle that we have been calling the point charge, and r is the distance that the point in space, at which we want to know E , is from the point charge that is causing E . Again, Coulomb’s Law is referred to as an inverse square law because of the way the magnitude of the electric field depends on the distance that the point of interest 1 is from the source charge. Now let’s talk about direction. Remember, the electric field at any point in space is a force-per- charge-of-would-be-victim vector and as a vector, it always has direction. We have already discussed the defining statement for the direction of the electric field: The electric field at a point in space is in the direction of the force that the electric field would exert on a positive victim if there were a positive victim at that point in space. This defining statement for the direction of the electric field is about the effect of the electric field. We need to relate this to the cause of the electric field. Let’s use some grade-school knowledge and common sense to find the direction of the electric field due to a positive source charge . First, we just have to obtain an imaginary positive test charge. I recommend that you keep one in your pocket at all times (when not in use) for just this kind of situation. Place your positive test charge in the vicinity of the source charge, at the location at which you wish to know the direction of the electric field. We know that like charges repel, so, the positive source charge repels our test charge. This means that the source charge, the point charge that is causing the electric field under investigation to exist, exerts a force on the test charge that is directly away from the source charge. Again, the

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Ch0203 - Chapter 3 The Electric Field Due to one or more...

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