- #1
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Homework Statement
I have a potential Value like ##V=V(x,y,z)+C##
I found ##\vec E## using partial derivative, like ##\vec E=((-∂V/∂x)i+(-∂V/∂y)j+(-∂V/∂z) k)##
Theres two position vectors,
##\vec r_{a}=2i##
##\vec r_{b}=j+k##
We need to find ##V_{ba}=?##
Homework Equations
##V_b-V_a=-\int_{r_{a}}^{r_{b}} \vec E⋅d\vec r##
##V_r=V(x_i,y_i,z_i)## where ##r=(x_i,y_i,z_i)##
The Attempt at a Solution
Ok I found E but since we are taking partial derivative the constant term disappeared.
I can find from ##V_b=V(0,1,1)## and ##V_a=V(2,0,0)## and the difference will be ##V_b-V_a=V_{ba}##
But If ı try to do this from ##V_b-V_a=-\int_{r_{a}}^{r_{b}} \vec E⋅d\vec r## using this.How can I approach the question.##\vec E## is a function of ##x,y,z## but we need a function of ##\vec r##
I mean the confusing part is,
##V_b-V_a=-\int_{r_{a}}^{r_{b}} ((-∂V/∂x)i+(-∂V/∂y)j+(-∂V/∂z) k)⋅d\vec r##
How can I take integral in this case ?
I ll do ##\vec E⋅\vec r_a-\vec E⋅\vec r_b## ??
And is my approach or answer is true..? , Is a constant term here makes a diffference ?