Electric field equation vs Electric potential equation??

[magicdock]

So electric field is the force a charge can exert on another charge at any given distance around it given by formula

E= kQ/d^2

Electric potential (voltage) is the amount of E.potential energy another charge can have at a distance from the original charge given by formula

V= kQ/d

my question is why is the d in electric potential not squared??

Is it because for electric potential we are assuming the field lines strength is uniform?

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[Formation]

One way to think about it is that Field is derived from Force, whereas Potential is derived from Potential Energy.

Field/force relate to the area of the applied field/force. Thus, they depend on d^2.

Potential/PE relate to the distance between two things. Thus, they just depend on d.

 

[betterfuture]

I think it is because electric potential is a property of the source charge that sets up the electric field. It is dependent on the location, so you are not really comparing it with another charge as you would with electrostatic force.

 

[magicdock]

I see. I even said it myself in the explanation lol thank you


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[aldol16]

Not sure if you want to get this deep into it, but it's because electric potential is the integral of -E*dr for a point charge and therefore when you do the integration, one of the r's drops out. It's analogous to finding the gravitational potential.