In a region, the electric potential varies as shown in the figure. Whi

In a region, the electric potential varies as shown in the figure. Which one among the following is the correct representation of the magnitude of the associated electric field ?

Graph (a)
Graph (b)
Graph (c)
Graph (d)
This question was previously asked in
UPSC Geoscientist – 2024
The correct option is A.
The electric field E is related to the electric potential V by the equation E = -dV/dx in one dimension. This means the electric field is the negative of the slope of the V-x graph.
In the given potential graph:
– From x=0 to x1, the potential V is constant. The slope dV/dx = 0. Therefore, the electric field E = -0 = 0.
– From x1 to x2, the potential V decreases linearly with increasing x. The slope dV/dx is constant and negative. Therefore, the electric field E = -(negative constant) = a constant positive value.
– From x2 to x3, the potential V is constant. The slope dV/dx = 0. Therefore, the electric field E = -0 = 0.
Graph (a) correctly represents these variations: zero field from 0 to x1, a positive constant field from x1 to x2, and zero field from x2 to x3.