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 = 4 m to r = 6 m
b. at r = 4 m
c. from r = 3 m to r = 4 m
d. from r = 0 m to r = 3 m

Answer 1

E = -dV / dr

i.e. the greater the rate of change of potential , the larger is the electric field at that point.
The rate of change of field is greatest from 3 to 4 . So E is maximum here.

Do not worry about minus sign in the above as it only of denoting the direction of the field which is vector quantity.

Answer 2

I see .. thanks