Electric Field Intensity in a Uniform Electric Field

To determine the electric field intensity in vector form, we need to analyze the given potentials at different points in the grid. By considering the potential differences between adjacent points, we can calculate the electric field intensity.

Step 1: Identifying the Points

Let's first identify the given points in the grid:

- O: Potential = 0 volts
- A: Potential = -1 volt
- B: Potential = -2 volts
- C: Potential = 1 volt
- D: Potential = 2 volts
- E: Potential = 0 volts
- F: Potential = -1 volt
- G: Potential = 1 volt
- H: Potential = 0 volts

Step 2: Calculating Potential Differences

Now, we will calculate the potential differences between adjacent points. The potential difference between two points (P1 and P2) is given by the equation:

ΔV = V2 - V1

We will use the convention that the electric field points from higher potential to lower potential.

- ΔV(OA) = V(A) - V(O) = (-1) - 0 = -1 volt
- ΔV(AB) = V(B) - V(A) = (-2) - (-1) = -1 volt
- ΔV(BC) = V(C) - V(B) = 1 - (-2) = 3 volts
- ΔV(CD) = V(D) - V(C) = 2 - 1 = 1 volt
- ΔV(DE) = V(E) - V(D) = 0 - 2 = -2 volts
- ΔV(EF) = V(F) - V(E) = (-1) - 0 = -1 volt
- ΔV(FG) = V(G) - V(F) = 1 - (-1) = 2 volts
- ΔV(GH) = V(H) - V(G) = 0 - 1 = -1 volt

Step 3: Calculating Electric Field Intensity

The electric field intensity (E) between two points is related to the potential difference (ΔV) by the equation:

E = -ΔV / d

where d represents the distance between the two points.

By comparing the potential differences between adjacent points and their distances (assuming each square has a side length of 1 meter), we can calculate the electric field intensity in vector form:

- E(OA) = -ΔV(OA) / d(OA) = -(-1) / 1 = 1 V/m (directed from A to O)
- E(AB) = -ΔV(AB) / d(AB) = -(-1) / 1 = 1 V/m (directed from B to A)
- E(BC) = -ΔV(BC) / d(BC) = -3 / 1 = -3 V/m (directed from C to B)
- E(CD) = -ΔV(CD) / d(CD) = -1 / 1 = -1 V/m (directed from D to C)
- E(DE) = -ΔV(DE) / d(DE) = -(-

In all 3 direction one by one find change in potential & then divide it by side length so we get e.f.in vector form