1.1 The integral form of Gauss's Law:
$\oint_{S}\;\vec{E}\;\circ\;\widehat{n}\;da = \frac{q_{enc}}{\varepsilon_0}$ ⇒ Gauss's Law for Electric Fields
The left side of this equation is a mathematical description of the electric flux - the number of electric field lines passing through a closed surface S, where as the right side is the total amount of charge contained within that surface divided by a constant called the permittivity of free space.
To understand the meaning of each symbol, here's an expanded view:
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| 1.1 The integral form of Gauss's Law |
Gauss's Law in integral form: Electric charge produces an electric
field and the flux of that field passing through any closed surface is
proportional to the total charge contained within that surface.
In other words: If you have a real & imaginary closed surface of any size & shape, and there is no charge inside the surface - the electric flux through the surface must be zero. If you were to place some positive (+ve)charge anywhere inside the surface - the electric flux through the surface would be positive. If you then added an equal amount of negative charge inside the surface (making the total enclosed charge zero), the electric flux would again be zero. Remember that it is the net charge enclosed by the surface that matters in Gauss's law.
1.2 The differential form of Gauss's Law:
$\nabla\;\circ\;E = \frac{\rho }{\varepsilon_0}$ ⇒ Gauss's Law for Electric Fields
The left side of this equation is a mathematical description of the divergence of the electric field - the tendency of the field to "flow" away from a specified location, and the right side is the electric charge density divided by the permittivity of the free space.
To understand the meaning of each symbol, here's an expanded view:
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1.2 The differential form of Gauss's Law
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Gauss's Law in differential form: The electric field produced by electric charge diverges from positive charge & converges upon negative charge.
In other words: The only places at which the divergence of the electric field is not zero are those locations at which charge is present. If positive (+ve) charge is present, the divergence is positive - meaning that electric field tends to "flow" away from that location. If negative charge is present, the divergence is negative - the electric field lines tend to "flow" towards that points.
In next note, we will discuss about "
Gauss's Law for Magnetic Fields"
