Electric Field Intensity due to Two Parallel Sheets of Charge Density

To determine the electric field intensity at a certain point due to two parallel sheets of charge density, we need to consider the superposition principle, which states that the total electric field at a point is the vector sum of the electric fields due to each individual charge distribution.

Given:
- Charge density of the first sheet = +6 C/m^2 (positive charge)
- Charge density of the second sheet = -6 C/m^2 (negative charge)

Steps to Calculate Electric Field Intensity:

1. Identify the Geometry:
- We have two parallel sheets of charge, which are infinitely large and lie parallel to each other.
- The first sheet has a positive charge density, and the second sheet has a negative charge density.

2. Derive the Electric Field Intensity Due to Each Sheet:
- The electric field intensity due to an infinitely large charged sheet is given by the formula: E = σ / (2ε₀), where σ is the charge density and ε₀ is the permittivity of free space.
- For the first sheet with positive charge density, the electric field intensity is E₁ = 6 / (2ε₀).
- For the second sheet with negative charge density, the electric field intensity is E₂ = -6 / (2ε₀).

3. Apply Superposition Principle:
- Since the electric fields due to each sheet are in opposite directions, we need to consider their algebraic sum.
- The total electric field intensity at the given point is the vector sum of E₁ and E₂: E_total = E₁ + E₂.
- The direction of the electric field depends on the signs and relative positions of the two sheets.

4. Calculate the Electric Field Intensity Magnitude:
- Substitute the values of E₁ and E₂ into the equation E_total = E₁ + E₂.
- Evaluate the expression to obtain the magnitude of the total electric field intensity at the given point.

5. Determine the Direction of the Electric Field:
- The direction of the electric field will be the direction of the total electric field intensity vector.
- If the magnitudes of E₁ and E₂ are equal, the electric field will be zero at the given point.
- If the magnitudes of E₁ and E₂ are different, the electric field will be in the direction of the stronger field.

By following these steps, you can determine the electric field intensity at a point due to two parallel sheets of charge density. Remember to consider the signs and relative positions of the sheets to determine the direction of the electric field.

Zero