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What is the difference between the two?

Physics Asked by 1500kook12 on February 11, 2021

Given a uniformly charged hemispherical shell of radius $R$, I want to calculate the potential at the center of the shell.
I can use the equation $V=kintfrac{sigma}{r}da$, where $sigma$ is the surface charge density, $r$ is the distance between the center and the surface element $da$
But can i calculate $vec E$ at the centre of the sphere and then use $V=-int vec E.vec {dl}$? Also, where should i place my reference point if the potential does not goes to $0$ at infinity?

One Answer

$V=kintfrac{sigma}{r}da$ gives automatically the potential difference between infinity and the centre.(as potential is assumed 0 to be at infinity )

Also, where should i place my reference point if the potential does not goes to 0 at infinity?

$V=-int vec E.vec {dl}$ gives the potential difference not the potential .

Potential is assumed 0 to be at infinity therefore you get potential at that point. If you assumed potential value to be say X at infinity then $V_{centre}-V_{infity}=V_{centre}-X$. In a short you can choose your reference point anywhere in the space but then you have to be careful using the standard formulae .

Answered by Danny LeBeau on February 11, 2021

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