Calculating Potential Difference in a Uniform Electric Field | Example Problem

[KillerZ]

I am wondering if I did this right.

Homework Statement

What is the potential difference between the points (x_i, y_i) = (0cm, -5cm) and (x_f, y_f) = (1cm, 4cm) in a uniform electric field equal to E = (20000i - 50000j) V/m ?

Homework Equations

$$\Delta V = V(s_{f})-V(s_{i}) = -\int^{s_{f}}_{s_{i}}E_{s}ds$$

E is uniform therefore:

$$\Delta V = - E_{s}\Delta s$$

$$\Delta s = \sqrt{(9cm)^{2}+(1cm)^{2}}$$

$$= \frac{\sqrt{82}}{100} m$$

$$E = \sqrt{(20000V/m)^{2}+(-50000V/m)^{2}}$$

$$= \sqrt{2.9*10^{9}} V/m$$

The Attempt at a Solution

$$\Delta V = - E_{s}\Delta s$$

$$= -(\sqrt{2.9*10^{9}} V/m)(\frac{\sqrt{82}}{100} m)$$

$$= -4876.5 V$$

 

[Delphi51]

Don't you have to take the angle into account? Only a component of E is in the direction of the distance.

 

[LowlyPion]

I think you take your

ΔV = E*Δs a little differently. Namely as the dot product of the E vector and the s vector, such that

ΔV = Ex*Δx i + Ey*Δy j