Potential Difference

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0
I am wondering if I did this right.

1. The problem statement, all variables and given/known data

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 ?

2. Relevant equations

[tex]\Delta V = V(s_{f})-V(s_{i}) = -\int^{s_{f}}_{s_{i}}E_{s}ds[/tex]

E is uniform therefore:

[tex]\Delta V = - E_{s}\Delta s[/tex]

[tex]\Delta s = \sqrt{(9cm)^{2}+(1cm)^{2}}[/tex]

[tex]= \frac{\sqrt{82}}{100} m[/tex]

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

[tex]= \sqrt{2.9*10^{9}} V/m[/tex]

3. The attempt at a solution

[tex]\Delta V = - E_{s}\Delta s[/tex]

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

[tex]= -4876.5 V[/tex]
 

Delphi51

Homework Helper
3,407
10
Don't you have to take the angle into account? Only a component of E is in the direction of the distance.
 

LowlyPion

Homework Helper
3,055
4
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
 

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