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.

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# Electric Potential

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