# Electric Potential

1. Nov 28, 2011

### humo90

I am confusing about dealing with the vectors in integral boundaries of the electric potential;
$^{b}_{a}$∫E.ds where a and b are vectors.
For example, if I would calculate the potential for outside region of a sphere along z-direction, I would use E=$\frac{ρR^3}{3ε_{0}z^2}$$\hat{z}$, and ds=dz$\hat{z}$
then V(r)=-$^{b}_{∞}$∫$\frac{ρR^3}{3ε_{0}z^2}$$\hat{z}$.dz$\hat{z}$ = -$^{b}_{∞}$∫$\frac{ρR^3}{3ε_{0}z^2}$.dz
After evaluating the integral which would be V(r)=[$\frac{ρR^3}{3ε_{0}z}$]$^{b}_{∞}$, say b=b$\hat{z}$, if I plug in b as magnitude the result would be as usual, but if b is vector, then how could I plug it in this potential function? Please help.

Last edited: Nov 28, 2011
2. Nov 30, 2011

### D'Alembert

Why do you plug the vector in it when you have just one component z. It is not V(r) but V(z), so that the vector is not needed.