It's crucial to specify the geometry of the infinitely charged object. The question could refer to an infinitely charged line, plane, or sphere. Therefore, I will address the infinitely charged plane as it is a common and well-defined scenario.
The electric field due to an infinitely charged plane is a uniform field, meaning it has the same magnitude and direction at all points in space.
Here's a breakdown:
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Assumptions: We assume a uniformly charged, infinitely large plane. This means the charge is evenly distributed across the entire surface, and the plane extends indefinitely in all directions.
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Formula: The electric field (E) is given by:
E = σ / (2ε₀)Where:
- σ (sigma) is the surface charge density (charge per unit area) of the plane.
- ε₀ (epsilon naught) is the permittivity of free space (approximately 8.854 x 10⁻¹² C²/Nm²).
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Direction: The electric field is perpendicular to the plane. If the plane has a positive charge density (σ > 0), the electric field points away from the plane. If the plane has a negative charge density (σ < 0), the electric field points towards the plane.
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Key Characteristics:
- Uniformity: The electric field's magnitude is independent of the distance from the plane. This is a direct consequence of the plane being infinite in extent.
- Perpendicularity: The electric field lines are always perpendicular to the surface of the charged plane.
- Symmetry: Due to the symmetry of the infinite plane, the electric field must point either directly away from or directly towards the plane.
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Derivation (Using Gauss's Law - Optional): To derive this formula, one typically uses Gauss's Law. A Gaussian surface in the shape of a cylinder is constructed, with its ends parallel to the charged plane. By applying Gauss's Law, we can relate the electric flux through the Gaussian surface to the enclosed charge, leading to the formula above.
In summary, the electric field created by an infinitely large, uniformly charged plane is a constant, uniform field perpendicular to the plane, with a magnitude proportional to the surface charge density and inversely proportional to twice the permittivity of free space.
