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2. Electric potential and capacitance — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics2. Electric potential and capacitance1 Mark
MCQ
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$
  • B
    $\frac{{ - 2}}{3}{X^2} - \frac{3}{2}{Y^2} + 5$
  • C
    $ - 2{X^2} - \frac{{3{Y^2}}}{2}$
  • D
    $\frac{{3{Y^2}}}{2} + 5$
✓

Answer

Correct option: A.
$ - {X^2} - \frac{3}{2}{Y^2} + 5$
a
$\int_{5}^{\mathrm{V}} \mathrm{dV}=-\int_{(0,0)}^{(\mathrm{X} , \mathrm{Y})} \mathrm{E} \cdot \mathrm{dr}=-\int_{0}^{\mathrm{X}} \mathrm{E}_{\mathrm{X}} \cdot \mathrm{dx}-\int_{0}^{\mathrm{Y}} \mathrm{E}_{\mathrm{Y}} \mathrm{dy}$

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

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

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