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2. Electric Potential and Capacitance
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The equation of an equipotential line in an electric field is $y = 2x$, then the electric field strength vector at $(1, 2)$ may be
A
$4 \hat i+ 3 \hat j$
B
$4 \hat i + 8 \hat j$
C
$8 \hat i + 4 \hat j$
D
$- 8 \hat i + 4 \hat j$
Solution
Electric field is perpendicular to equipotential line
$\because \quad y=2 x$
or $\quad \frac{d y}{d x}=2$
$\therefore \quad \mathrm{m}_{1}=2$
$\therefore \quad \mathrm{m}_{1} \mathrm{m}_{2}=-1$
$\mathrm{m}_{2}=-\frac{1}{2}$
$\therefore$ $\tan \theta=-\frac{1}{2}$
where $\theta$ is angle with $x$ $-axis.$
$\tan \theta=\frac{4}{-8}=-\frac{1}{2}$
Standard 12
Physics
