Potential From an Electric Field

[snoweangel27]

I have been trying to calculate the potential difference between to points. In doing so, I have tried taking $$\int$$ -E * dl, in which I end up with -E*4, but that does not include the point charge, and I'm just not sure what I need to do to Calculate the potential with the addition of the point charge.

Question
A uniform electric field of 8 kN/C is in the x direction. A positive point charge Q = 3 micro Coloumbs is released from rest at the origin.
--What is the potential difference V(4 m) - V(0)?

 

[Doc Al]

You're doing OK. The potential difference only depends on the field, not on the charge you are putting in the field. (I suspect there will be addition questions for this problem where you will need to use the charge.)

 

[Moetasim]

I understand your confusion in trying to calculate the potential difference between two points in an electric field. It seems like you have attempted to use the equation V = -∫E*dl, which is the correct equation for calculating potential difference in an electric field. However, there are a few things to consider in order to properly calculate the potential difference in this scenario.

Firstly, the equation V = -∫E*dl assumes that the electric field is constant along the path of integration. In this case, the electric field is uniform in the x direction, so this assumption is valid. However, you also need to consider the direction of the path you are integrating. Since the electric field is in the x direction, the path of integration should also be in the x direction.

Secondly, the equation V = -∫E*dl does not take into account the presence of a point charge. This equation only considers the electric field created by a continuous distribution of charge. In order to account for the point charge, you need to use the equation V = kQ/r, where k is the Coulomb's constant, Q is the point charge, and r is the distance between the point charge and the point at which you are calculating the potential.

So, to calculate the potential difference between two points in an electric field with the addition of a point charge, you need to first calculate the potential difference using the equation V = -∫E*dl, and then add the potential due to the point charge using the equation V = kQ/r.

In this specific scenario, the potential difference V(4 m) - V(0) can be calculated as follows:

- First, calculate the potential difference using V = -∫E*dl. Since the electric field is uniform in the x direction, the path of integration should also be in the x direction. So, we can write V(4 m) - V(0) = -∫E*dl from x = 0 m to x = 4 m. Since E = 8 kN/C in the x direction, the integral becomes V(4 m) - V(0) = -8 kN/C * ∫dx from x = 0 m to x = 4 m. Evaluating the integral, we get V(4 m) - V(0) = -8 kN/C * (4 m - 0 m) =