- #1
kacete
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Homework Statement
Given the Electric field [tex]\vec{E}=z\vec{u_{x}}-3y^{2}\vec{u_{y}}+x\vec{u_{z}} V/m[/tex] find the necessary Work to move a charge [tex]Q=7\mu C[/tex] along an incremental path of [tex]1mm[/tex] distance in the direction of [tex]2\vec{u_{x}}-6\vec{u_{y}}-3\vec{u_{z}}[/tex] which locates in [tex]P(1,2,3)[/tex]
Homework Equations
Work
[tex]W=-Q\int^{f}_{i}\vec{E}.d\vec{l}[/tex]
i - inicial point
f - final point
Solution
[tex]W=-75nJ[/tex]
The Attempt at a Solution
Converting to base units
[tex]Q=7\mu C=7x10^{-6}C[/tex]
[tex]d=1mm=1x10^{-3}m[/tex]
The electric field at the given point
[tex]\vec{E}=3\vec{u_{x}}-12\vec{u_{y}}+1\vec{u_{z}} V/m[/tex]
The equation
[tex]W=-Q\int^{f}_{i}\vec{E}.d\vec{l}=-Q.E\int^{f}_{i}dl.(2\vec{u_{x}}-6\vec{u_{y}}-3\vec{u_{z}})[/tex]
where [tex]\int^{f}_{i}dl=1x10^{-3}[/tex]
My solution
[tex]W=-525nJ[/tex]
Where did I go wrong?