Now, once we determine the electric field generated by this incremental charge at this location, then we can go ahead and calculate the electric field due to the next incremental charge at the same location. Relative to this coordinate system, then, our incremental charge will be located x distance away from the origin, and the thickness of this incremental charge will be dx, just a little increment from that position.Īnd of course this dx is very, very small, so that we can treat the amount of charge along the length of dx, dq, like a point charge. Let us assume the other end of rod is located at the origin.
Since we’re dealing with a one dimensional case, we’re going to introduce an x-coordinate system. Let’s introduce a coordinate system to our problem. Therefore the electric field generated by this dq, at this location, will be pointing to the right and will have magnitude of incremental field of d E. It is a positive charge and it will generate a electric field at the point of interest and radially outward direction. Therefore the problem induces into a form that we have a point charge sitting over here, with a magnitude of dq. When we look at the form of distribution, we see that it is linear charged distribution, charge is distributed along the length of the rod and to be able to calculate the electric field of charged distribution, first we choose an incremental charge amount within the distribution at an arbitrary location, and treat the amount of the charge associated with that segment as incremental charge and treat it like a point charge. We’re interested with the electric field that it generates a distance away from one end of the rod at this point, P, our point of interest. We have a finite length rod with a length of, L, and this is positively charged and the charged is distributed uniformly along its length. Let’s say, a, distance from one end of the rod. Let’s say, with length, L, and charge, Q, along it’s axis.
Let’s try to calculate the electric field of this uniformly charged rod.
From Office of Academic Technologies on Vimeo.Įxample 1- Electric field of a charged rod along its AxisĪs a first example for the application of Coulomb’s law to the charge distributions, let’s consider a finite length uniformly charged rod.
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