Electric Potential: V=-ED for Capacitors?

In summary, the change in electric potential between two capacitors can be represented by the equation V=-ED, where V is the change in potential, E is the electric field, and D is the displacement between the two plates. This equation takes into account the direction of the electric field and displacement, resulting in a negative value for the change in potential in a capacitor, as the electric field points from the higher potential to the lower.
  • #1
collegeconfid
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Homework Statement


Why is the change in the electric potential between two capacitors V=ED ?


Homework Equations



V=-ED

The Attempt at a Solution



Isn't the change in electric potential equal to the negative of the product of the electric field and displacement?
So, why is it that for a capacitor the change in potential is not V=-ED ?

Thanks for any help.
 
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  • #2
You mean the change in potential between the 2 plates of a capacitor?

Actually the equation [itex] \Delta V = -E \cdot D [/itex] is satisfied

[itex] E \cdot D [/itex] is the dot product of the vectors of the electric field and the displacement.
It's +|E||D| if they are in the same direction and -|E||D| if they are in opposite directions.

(|E| is the magniture of the electric field |D| is the magnitude of the displacement)

In a capacitor, the electric field points from the positive plate to the negative, so from the higher potential to the lower. If you move in the direction of the electric field, then both E and D have
the same direction, but you're moving to a lower potential, which is as it should because [itex] -E \cdot D [/itex] is negative
 

FAQ: Electric Potential: V=-ED for Capacitors?

What is the definition of electric potential for capacitors?

Electric potential is the measure of the potential energy per unit charge at a certain point in an electric field. For capacitors, the electric potential is described by the equation V=-ED, where V is the potential difference, E is the electric field strength, and D is the distance between the capacitor plates.

How is the electric potential related to the capacitance of a capacitor?

The electric potential is directly proportional to the capacitance of a capacitor. This means that as the capacitance increases, the electric potential also increases. The equation for this relationship is V=Q/C, where Q is the charge on the capacitor and C is the capacitance.

What role does the distance between capacitor plates play in the electric potential?

The distance between capacitor plates, denoted by D in the equation V=-ED, is a crucial factor in determining the electric potential. As the distance between the plates increases, the electric potential decreases. This is because a larger distance results in a weaker electric field and a smaller potential difference.

How does the electric potential affect the energy stored in a capacitor?

The electric potential plays a significant role in the energy stored in a capacitor. The higher the electric potential, the more energy can be stored in the capacitor. This is because the potential difference between the plates determines the amount of work needed to move charges from one plate to the other, and this work is stored as potential energy in the capacitor.

Can the electric potential of a capacitor be negative?

Yes, the electric potential of a capacitor can be negative. This occurs when the electric field is directed in the opposite direction of the positive plate. In this case, the potential difference is negative, which is reflected in the equation V=-ED. However, the magnitude of the potential is still positive, meaning that the electric potential energy is still stored in the capacitor.

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