Following figure indicates the electric potential V as a function through 4 regions on x-axis. Which of the following is correct for the electric field E in these regions?
Show Hint
Field is minus the slope of the V-x graph. Flat parts give zero field, and the steeper part gives the larger field.
Step 1: Read the slopes
Field strength is $|E|=\left|\frac{\Delta V}{\Delta x}\right|$. So we compare the steepness of the four segments of the graph.
Step 2: Flat segments
Regions 1 and 3 have no change in $V$, so $E=0$ in both. They are equal.
Step 3: Sloping segments
Region 2 climbs from a nonzero value $V_B$ up to $V_C$, so its rise is $V_C-V_B$. Region 4 drops from $V_C$ all the way to $0$, so its fall is larger, $V_C$. The line in region 4 is also steeper in the picture. So $E_4>E_2$.
Step 4: Pick the option
The statement that matches $E_1=E_3=0$ and $E_2<E_4$ is option (C).
Final Answer:
Option (C) is correct.
\[ \boxed{E_1=E_3,\ E_2<E_4} \]
