The graph in the figure shows the variation of the electric potential V (measured in volts)as a function of the radial direction r (measured in meters).For which range or value of r is the magnitude of the electric field the largest?
A) from r = 0 m to r = 3 m
B) from r = 3 m to r = 4 m
C) from r = 4 m to r = 6 m
D) at r = 3 m
E) at r = 4 m

Question

The graph in the figure shows the variation of the electric potential V (measured in volts)as a function of the radial direction r (measured in meters).For which range or value of r is the magnitude of the electric field the largest? 
A) from r = 0 m to r = 3 m 
B) from r = 3 m to r = 4 m 
C) from r = 4 m to r = 6 m 
D) at r = 3 m 
E) at r = 4 m

Quizplus · Accepted Answer

The electric field is given by the negative gradient of the electric potential, i.e., E = -dV/dr. The magnitude of the electric field is largest where the slope of the electric potential is steepest. From the graph, we see that between r = 3 m and r = 4 m, the slope of the curve is the steepest, indicating the largest magnitude of the electric field in this range. Hence, choice B is the correct answer.

The Graph in the Figure Shows the Variation of the Electric