Find the Electric Field if Electric Potential is given at two PointsHelp needed

[nishantve1]

Homework Statement

Given that on the x-axis on at -1 the V is 120V at the point +1 V is 80 V . What is the Electric field at the origin (0,0)
OPTIONS
a)must be equal to 20
b)may be equal to 20
c)may be greater than 20
d)may be less than 20

Homework Equations

The Attempt at a Solution

I did this V(-1) - V(1) = integral from -1 to 1 (E.dr)
On Solving
E = 20 V/cm

but not sure what's its value at the origin ? According to me it should be less than or equal to 20 but the answer says Greater than or equal to 20 How ?

 

[anathema]

you are correct in your approach to solving this problem. The electric field at the origin can be found by taking the limit of the integral as the distance between the two points approaches 0. This will give us the electric field at that exact point.

In this case, the electric field at the origin will be equal to 20 V/cm, as you have correctly calculated. This means that the correct answer is option a) must be equal to 20.

Although the electric field at the origin is equal to 20 V/cm, it is important to note that the electric field may be greater than 20 V/cm at other points in the region. This is because the electric field is a vector quantity and can vary in magnitude and direction at different points.

In conclusion, the electric field at the origin is equal to 20 V/cm and the correct answer is option a) must be equal to 20.