# Calculating Potential Difference Between A(0,1) & B(1,0)

In summary, the problem involves calculating the potential difference between points A(0,1) and B(1,0) using the electric field vector E=x(1-sin (phi))+ y.cos(phi), where x and y are unit vectors. The two given paths to consider are a circular arc and a straight line connecting the two points. The potential difference can be calculated using the formula V = -∫E·dL, with the line equation potentially being helpful in finding the solution for the second question.

Hi, I would like to have some suggestion about how to do this problem:

Given the electric field vector E=x(1-sin (phi))+ y.cos(phi)
x and y are unit vectors.
Calculate the potential difference between the points A(0,1) and B(1,0).
along :

1- Circular arc from(0,1) to (1,0)

2-straight line connecting (0,1) and (1,0)

thank you.

V is the path integral of E dot dL, with a minus sign(convention).

I have succeeded to do the first question but how to do the second one. I found the line equation( I think it can help) but then I don't know how to continue.

B.

## 1. How do you calculate potential difference between two points?

To calculate the potential difference between two points, you need to subtract the potential at one point from the potential at the other point. The formula for potential difference is V = V2 - V1, where V2 is the potential at the second point and V1 is the potential at the first point.

## 2. What are the units for potential difference?

Potential difference is measured in volts (V). It represents the amount of electric potential energy per unit charge at a specific point in an electrical circuit.

## 3. Can potential difference be negative?

Yes, potential difference can be negative. This occurs when the potential at the first point is greater than the potential at the second point. In this case, the electric charge would flow from the first point to the second point, resulting in a negative potential difference.

## 4. What information do you need to calculate potential difference between two points?

To calculate potential difference between two points, you need to know the potential at each point and the direction of the electric field. You also need to know the distance between the two points.

## 5. How does the potential difference between two points affect the flow of electric charge?

The potential difference between two points determines the strength and direction of the electric field, which in turn affects the flow of electric charge. A greater potential difference means a stronger electric field, which will cause electric charges to flow more quickly and with more force.