If is zero throughout a certain region of space, is the potential necessarily also zero in this region? Why or why not? If not, what canbe said about the potential?

The potential difference (which is the same as voltage) is equal to the amount of current multiplied by the resistance. A potential difference of one Volt is equal to one Joule of energy being used by one Coulomb of charge when it flows between two points in a circuit.

Given:

The electric field vector is along a path from point A-

Required:

Finding the potential difference between the two points-

Finding if the electric field vector is zero everywhere along any path from A to B -

Step 2

Solution:

As we know the electric field is a conservative ?led- Also, We know that the electric ?led is given by the following relation:

Rearrange and integrate along the given path from point A to point B:

Then we get

So, the potential difference between the No points is equal to an arbitrary constant due to the zero electric field everywhere along the two points path, is not equal to zero.

Therefore

The potential difference betWeen the two points is equal to an arbitrary constant due to the zero electric field everywhere along the tWO points path, is not equal to zero.