Question

If E is zero everywhere along a certain path that leads from point Ato point B, what is the potential difference between those two points? Does this mean that Eis zero everywhere along anypath from A to B? Explain.

Short answer

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-

Step-by-step solution

About potential difference

The electric potential difference between points A and B, VB−VA 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.

Determine the potential difference between two points

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-

Determine the E is zero everywhere

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-