I am confusing about dealing with the vectors in integral boundaries of the electric potential;(adsbygoogle = window.adsbygoogle || []).push({});

[itex]^{b}_{a}[/itex]∫E.dswhere a and b are vectors.

For example, if I would calculate the potential for outside region of a sphere along z-direction, I would useE=[itex]\frac{ρR^3}{3ε_{0}z^2}[/itex][itex]\hat{z}[/itex], and ds=dz[itex]\hat{z}[/itex]

then V(r)=-[itex]^{b}_{∞}[/itex]∫[itex]\frac{ρR^3}{3ε_{0}z^2}[/itex][itex]\hat{z}[/itex].dz[itex]\hat{z}[/itex] = -[itex]^{b}_{∞}[/itex]∫[itex]\frac{ρR^3}{3ε_{0}z^2}[/itex].dz

After evaluating the integral which would be V(r)=[[itex]\frac{ρR^3}{3ε_{0}z}[/itex]][itex]^{b}_{∞}[/itex], sayb=b[itex]\hat{z}[/itex], if I plug in b as magnitude the result would be as usual, but ifbis vector, then how could I plug it in this potential function? Please help.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Electric Potential

**Physics Forums | Science Articles, Homework Help, Discussion**