Electric field intensity at a point due to two parallel sheets of char...
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.
Electric field intensity at a point due to two parallel sheets of char...
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