For given vec E = 2xhat{i} + 3yhat{j} , potential at (X, Y) if potential at origin is 5, volts.

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2. Electric Potential and Capacitance

medium

For given $\vec E = 2x\hat i + 3y\hat j$, find the potential at $(X, Y)$ if potential at origin is $5\, volts.$

$ - {X^2} - \frac{3}{2}{Y^2} + 5$

$\frac{{ - 2}}{3}{X^2} - \frac{3}{2}{Y^2} + 5$

$ - 2{X^2} - \frac{{3{Y^2}}}{2}$

$\frac{{3{Y^2}}}{2} + 5$

Solution

$\int_{5}^{\mathrm{V}} \mathrm{dV}=-\int_{(0,0)}^{(\mathrm{X} , \mathrm{Y})} \mathrm{E} \cdot \mathrm{dr}=-\int_{0}^{\mathrm{X}} \mathrm{E}_{\mathrm{X}} \cdot \mathrm{dx}-\int_{0}^{\mathrm{Y}} \mathrm{E}_{\mathrm{Y}} \mathrm{dy}$

$V-5=\frac{-2 X^{2}}{2} \frac{-3 Y^{2}}{2}$

$V=\frac{-2 X^{2}}{2} \frac{-3 Y^{2}}{2}+5$

Standard 12

Physics

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(AIPMT-2014)

For given $\vec E = 2x\hat i + 3y\hat j$, find the potential at $(X, Y)$ if potential at origin is $5\, volts.$

Solution

Similar Questions

In a hollow spherical shell potential $(V)$ changes with respect to distance $(r)$ from centre

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