Let’s talk about electric fields. Electric fields and magnetic fields are important for engineers and scientists to understand.
Looking at Coulomb’s Law, we see that a point charge will cause a force on another point charge. This force is sent through the electric field of the two point charges.




The vector magnitude of an electric field is equal to the vector force we calculated in Coulomb’s Law divided by the unit charge experienced by the reference point which gives E.hat = F.hat/q
One important mathematical concept that must be explored is that of a radial vector. This is also called a vector field. A radial vector is a vector that exists on a polar field as opposed to a Cartesian field. This vector will point from the center outward along the radial lines of a sphere. When describing an electric field, it exists as a radial vector. Describing the electric field at a point works using the following equation:

This vector will always point away from a positive charge and always point inward towards a negative charge.  In this equation, q is the charge at that given point, E0 is the given permitivity of free space, and r is the distance to the reference point. This is all multiplied by the radius vector in order to put it in radial vector form. If you’re not familiar with polar coordinates and vectors, don’t worry. You’ll get to it in vector calculus!
 
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