The figure below shows two points in an E-field:

Point 1 is at (X1,Y1) = (3,4) in m, and
Point 2 is at (X2,Y2) = (12,9) in m.
The Electric Field is constant, with a magnitude of 68 V/m, and is directed parallel to the +X-axis. The potential at point 2 is 588 V. Calculate the potential at point 1.

I get that V = Er but I'm kinda lost on the exact steps to go from potential 2 to potential 1

Skírtar falhüler

To calculate the potential at point 1 using the given information, you can use the concept of potential difference and the formula for electric potential. Here are the steps:

1. Determine the distance between the two points, point 1 and point 2. You can use the distance formula:
Distance = √((X2 - X1)^2 + (Y2 - Y1)^2)

Substituting the values:
Distance = √((12 - 3)^2 + (9 - 4)^2)
Distance = √(9^2 + 5^2)
Distance = √(81 + 25)
Distance = √106
Distance ≈ 10.29 m

2. Compute the potential difference (V₂ - V₁) between point 2 and point 1 using the potential difference formula:
V₂ - V₁ = E · Distance

Substituting the known values:
V₂ - V₁ = 68 V/m · 10.29 m
V₂ - V₁ = 699.72 V

3. Rearrange the equation to solve for V₁:
V₁ = V₂ - (E · Distance)
V₁ = 588 V - (68 V/m · 10.29 m)
V₁ = 588 V - 700.92 V
V₁ ≈ -112.92 V

Therefore, the potential at point 1 is approximately -112.92 V.