Electrostatics is a branch of physics that studies forces between static (non-moving) electric charges. One of the key concepts in electrostatics is the electrostatic field, often referred to as the electric field. An electric field defines the space surrounding a charged particle in which other charges feel an electrostatic force.
Electric field intensity, denoted by E, is a vector quantity that defines the force per unit charge at a point in space due to a source charge. It represents both the magnitude and orientation of the electric field at a given point.
Mathematically, the electric field intensity is given by:
\( \vec{E} = \frac{\vec{F}}{q} \)
Where:
When calculating the field due to a point charge \( Q \) at a distance \( r \), the magnitude of the electric field is:
\( E = \frac{1}{4\pi\varepsilon_0} \cdot \frac{Q}{r^2} \)
Here, \( \varepsilon_0 \) is the permittivity of free space and has a value of approximately \( 8.854 \times 10^{-12} \, {C}^2/ {N·m}^2 \).
This is a crucial equation in electrostatics. It establishes the relationship between the electric field and the force acting on a charge:
\( \vec{F} = q\vec{E} \)
This equation shows that the force experienced by a charge is directly proportional to both the magnitude of the charge and the electric field it is placed in. The direction of the force depends on the sign of the charge.
Similar to how gravity applies a force on a mass through the equation \( F = mg \), with \( g \) representing gravitational field strength, an electric field applies force on a charge via \( F = qE \). Both follow the same conceptual framework:
When multiple charges are present, the total electric field at a point is calculated using the principle of superposition. It explains that the overall electric field is obtained by vectorially adding the electric fields produced by each individual charge.
\( \vec{E}_{net} = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 + \cdots \)
In other words, each electric field is combined by considering both its size and the direction it points. For example, if two equal charges are placed symmetrically, their fields may cancel or reinforce depending on their direction.
The SI unit of electric field intensity is newton per coulomb (N/C) or volt per meter (V/m). The dimensional formula is:
\( [E] = MLT^{-3}A^{-1} \)
Understanding the electrostatic field and its intensity is foundational for solving problems in electrostatics. The equations \( F = qE \) and \( F = mg \) help bridge concepts between electricity and mechanics, while the superposition principle enables accurate calculation of electric fields from multiple sources—an essential skill in the study of physics.
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