Hi, I was wondering how to calculate both a force and an electric field when you're only given one charge. For example, if I have a positive test charge q, and a positive charage Q1 r distance away from the test charge... I'm confused on how I can calculate the force vector (resultant) in order to set up a triangle and find the x and y components of the force (same for electric fields).
If you are given only one charge, and no electric field anywhere due to some other arrangement of charges, then all you can do is calculate the electric field due to that one charge. In this case, you can determine the electric field at a point some distance (r) away. The direction of the electric field will be the same as a force would be on a positive charge if you put one there, but the magnitude of this test charge (q) is divided out (E=F/q). Remember that for a point charge, the electric field points radially outward/inward from the positive/negative charge. This makes sense if you think about putting a positive test charge anywhere around the charge you are given, as the force between the two will be along the direction of the separation.
You might also be asked about a charge in an electric field (usually a uniform one, since that's easiest to deal with). In this case you can determine the force on the charge due to this external electric field by making use of the definition of electric field: E=F/q. Flip this around, and you have: F=Eq, which can be very useful. Let's say you have an electron in a 1 V/m (N/C) uniform electric field pointing north. The magnitude of the force on the electron will be: F=(1N/C)(1.6e-19C)=1.6e-19N. The direction of the force will be south, since the electron is negatively charged and the direction of E is defined as the direction of force on a positive charge.
I hope this helps, please follow-up if I haven't answered your question here.
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