# Potential lowering effect on a positively-charged plate

Suppose the following situation:

A positively-charged plate, not connected to any e.m.f. source, is brought near a neutral block of conductor material. Naturally, negative charges are induced on the side of the conductor material that is closer to the plate.

I would like to ask what is the change to the potential of this positively-charged plate due to the induced negative charges on the conductor material.

My physics teacher has been trying to convince me that the plate's positive potential decreases as he tells me that the electric field created by the induced negative charges causes the potential of everything in its vicinity to be lowered.

However, I intuitively thought that the potential of the positively-charged plate should increase since the induced negative charges would repel negatively-charged particles in the plate and cause the side of the plate closer to the induced negative charges to become more positively-charged, increasing its positive potential.

• This is basically method of image charges Commented May 20, 2020 at 12:20

## 2 Answers

The potential difference between two points equals the work required per unit charge to move the charge between the points. For a uniform electric field $$E$$ the work required to move a charge $$Q$$ a distance $$d$$ is $$QEd$$. Therefore the potential difference between the points is $$Ed$$.

The polarization of the previously neutral conductive block creates an electric field in the block opposing the field of the positively charged plate, though there is no net field within the block. This reduces the effective electric field of the positively charged plate. The phenomena is similar to the effect of the polarization of a dielectric between capacitor plates that reduces the effective field between the plates. For a discussion of this refer to the following link:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/dielec.html

Since the effective field $$E$$ of the positively charged plate is reduced, the potential difference between two points in the field is reduced.

Your physics teacher is correct.

Hope this helps.

Your teacher is correct.

The induced positive charges in parts of the plate near the block leave behind negative charges in parts of the plate far away from the block. The positive charges increase the potential of the plate and the left-behind negative charges decrease the potential of the plate. These two effects negate each other.

From the plate's perspective, the polarized block can be treated as a small negative charge. This slightly decreases the electric potential inside of the plate.

• The plate could be positively charged without any electrons on it. Commented Jun 9, 2019 at 11:30
• If the two opposing effects negated each other, then there wouldn't be any change to the potential of the plate? Commented Jun 9, 2019 at 16:06