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The electric potential difference between points A and B, VB鈭扸A is defined to be the change in potential energy of a charge q moved from A to B, divided by the charge. Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta.

Given:

The electric f?ed vector is along a path from point A-

Required:

Finding the potential difference between the Mo points-

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

Solution:

As we know the electric ?eld 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:

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

Then We get

So, the potential difference between the Mo points is equal to an arbitrary constant due to the zero electric Field everywhere along the two points path-

Calculation:

As we know the electric field is a conservative field- So, the value of the electric field betWeen the tWO-point is independent on the path- So, the electric field remaining zero everywhere along any path from A to B-

Therefore

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-

The value of the electric field betWeen the tWO-point is independent on the path- So, the electric field remaining zero everywhere along any path from A to B-