Electrice field and force equations clarification

[Little Etoile]

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If E by q= (k*Q)/r^2, and Electric Force= (k*q1*q2)/r^2, and F on q= qE, then doesn’t F on q expand to= (k*q*Q)/r^2, which is the same as the electric force equation before it? What’s the difference, if any, except that instead of referring to the second and first charge by number, they are referred to by as the source charge and probe charge? Same result though, right? So why do they have two equations for it? Am I missing something?



Thanks in advance!

 

[pyromatic]

You're right; there is no difference. The subscript is left off in the equation for an electric field because you're usually interested in the field itself, not the particular charge arrangement(s) that yield the field. And you should also take note that in situations where you're doing the whole "F = k*q1*q2/r^2" thing, the force is applied to both charges, whereas when working with electric fields, you're taking the limit of the test charge to zero so that the field remains undisturbed.