Voltage and Force - Electric Charge

[reising1]

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From point charges, we can see that
Electric field (E) = integral of Voltage (V)

that is,
E = kq/r^2
V = kq/r

But when we look at voltage due to moving a charge a distance d, it seems to be the opposite
V = integral of E

that is,
V = Ed
To think of it differently, voltage is the area under a graph of E and d

So what's going on here?

 

[Deadlifts]

From point charges, we can see that
Electric field (E) = integral of Voltage (V)

that is,
E = kq/r^2
V = kq/r

But when we look at voltage due to moving a charge a distance d, it seems to be the opposite
V = integral of E

that is,
V = Ed
To think of it differently, voltage is the area under a graph of E and d

So what's going on here?

You can get the V = Ed equation from the point charge equations.

Vr=kq
E = Vr / r^2
E = V / r
Er = V

I'm not sure where you're conceptually having issues?