Question

$V_{0}$ is theΒ potential at the origin in an electric field.Β $E=E_{x}iβE_{y}jβ$. The potential at the point (x,y) is:

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Solution

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Correct option is A)

$V(x_{1})βV(x_{2})=β«_{x_{1}}Edx.$

Now potential change in x direction

$V_{x}(x)βV_{x}(o)=β«_{x}E_{x}dx=βE_{x}x.$

$V_{x}(x)=V_{x}(o)βE_{x}x$

Potential change in y direction

$V_{y}(y)βV_{y}(o)=β«_{y}(βE_{y})dy=+E_{y}y$

$V_{y}(y)=V_{y}(o)+E_{y}y$

Now total potential at (x,y)

$=V_{x}+V_{y}$

$=V_{x}(o)βE_{x}x+V_{y}(o)+E_{y}y$

$=V_{o}βxE_{x}+yE_{y}$

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