I am studying capacitors in an electromagnetism course and I am having trouble understanding/deriving the equation for voltage.(adsbygoogle = window.adsbygoogle || []).push({});

We have a spherical capacitor with a positive charge on the surface on the center conductor (sphere radius R1), and negative charge on the outer conductor (sphere radius R2), and we have found the equation for the Electric Field using Gauss's law, and now we want to integrate to find the voltage.

We want to find the equation for the voltage between the two conductors as a function of some arbitrary radius (r), so we integrate the electric field from R2 to r.

My question is, would integrating from r to R1 be incorrect? My professor seems to think so but he isn't doing a good job on helping me understand why.

In my years of working with voltage, you have always have a reference point when measuring it, and if your leads backwards, you just get a negative voltage.

I tried both ways (integrating from R2 to r and integrating from r to R1), and then used these equations to find the total voltage needed to establish the field:

Vtotal = V(R1)-V(R2)

And this yielded the same result in either case....so what makes integrating from R2 to r correct and integrating from r to R1 incorrect?

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# Spherical Capacitor, equation for voltage

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