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2. Electric Potential and Capacitance
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Electric field at a point $(x, y, z)$ is represented by $\vec E = 2x\hat i + {y^2}\hat j$ if potential at $(0,0,0)$ is $2\, volt$ find potential at $(1, 1, 1)$
A
$\frac{4}{3}$
B
$\frac{2}{3}$
C
$\frac{10}{3}$
D
$\frac{1}{3}$
Solution
$\mathrm{V}-\mathrm{V}_{(0,0,0)}=\int_{0}^{1} \mathrm{E}_{\mathrm{x}} \mathrm{d} \mathrm{x}+\int_{0}^{1} \mathrm{E}_{\mathrm{y}} \mathrm{d} \mathrm{y}$
$\mathrm{V}-2=\left[\mathrm{x}^{2}\right]_{0}^{1}+\frac{1}{3}\left[\mathrm{y}^{3}\right]_{0}^{1}$
$\mathrm{V}=2+1+\frac{1}{3}=\frac{10}{3} \mathrm{\,volt}$
Standard 12
Physics
