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2. Electric Potential and Capacitance
medium
$10^{-3}\;\mu C$ ના વિદ્યુતભારને $x - y$ યામપદ્ધતિના ઉગમબિંદુ પર મૂકેલો છે. બે બિદુઓ $A (\sqrt{2}, \sqrt{2})$ અને $B (2,0)$ વચ્ચેનો વિદ્યુતસ્થિતિમાનનો તફાવત ($V$ માં) કેટલો હશે?
A
$4.5$
B
$9$
C
$0$
D
$2$
(AIEEE-2007)
Solution

The distance of point $A(\sqrt{2}, \sqrt{2})$ from the origin,
$OA=\left|\vec{r}_{1}\right|=\sqrt{(\sqrt{2})^{2}+(\sqrt{2})^{2}}=\sqrt{4}=2$ units.
The distance of point $B(2,0)$ from the origin,
$O B=|\overrightarrow{r_{2}}|=\sqrt{(2)^{2}+(0)^{2}}=2$ units.
Now, potential at $A, V_{A}=\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{Q}{(O A)}$
Potential at $B, V_{B}=\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{Q}{(O B)}$
$\therefore $ Potential difference between the points $A$ and $B$ is zero.
Standard 12
Physics