Q.
The figure shows electric potential V as a function of $x$. Rank the four regions according to the magnitude of $x$-component of the electric field E within them, greatest first
A) $E_{4} > E_{2} > E_{3} > E_{1}$
B) $E_{2} > E_{4} > E_{1} = E_{3}$
C) $E_{1} > E_{2} > E_{3} > E_{4}$
D) $E_{1} > E_{3} > E_{2} > E_{4}$
Explanation
(b) Electric field
$E = - \frac{dV}{dx}$
For I region, $V_{1}$=constant
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$\therefore\ \ \frac{dV_{1}}{dx} = 0\ $
$\therefore\ \ \ \ E_{1} = 0\ $
For II region,
$V_{2} = + ve = + f(x)$
$\therefore E_{2} = - \frac{dV_{2}}{dx} = - ve$
For III region.
$V_{3}$=constant
$\therefore\ \frac{dV_{3}}{dx} = 0\ \ $
$\therefore\ \ \ E_{3} = 0\ $
For IV region, $V_{1} = - f(x)$
$\therefore\ \ \ E_{4} = - \frac{dV_{4}}{dx} = + ve$
From these values, we have
$E_{2} > E_{4} > E_{1} = E_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.