- #1
jaguar7
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Homework Statement
Electric Potential from Electric Field
Suppose that, as a function of x, y, and z, an electric field has the following components:
Ex = 6x^2y, Ey = 2x^3 + 2y and Ez = 0
where E is measured in V/m and the distances are measured in m. Find the electrical potential difference between the origin and the point x = -0.4 m, y = 6.1 m, z = 0.0 m.
Homework Equations
The Attempt at a Solution
We should be able to just do E dot r, which gives (6x^2y)x + (3x^3+2y)y, where x = -.5 and y = 6.1
this didn't work.
Reattempt:
for reference: Ex = 6x^2y, Ey = 2x^3 + 2y, x = -0.4 m, y = 6.1 m
dV = integral E dot dr from 0 to the point = integral Ex dx from 0 to -.4 + integral Ey dy from 0 to 6.1
= integral 6x^2y dx from x=0 to -.4 + integral 2x^3 + 2y from y=0 to 6.1
= y*2x^3 |(x=0 to -.4) + (2x^3y + y^2)|(y=0 to 6.1)
=2(-.4^3)y + (12.2x^3 + 6.1^2),
where x = -.4 and y=6.1
plug in and get 35.6V,
wrong...