Question
State the important points of Gauss's law.
✓
Answer
►(i) Gauss's law is true for any closed surface, no matter what its shape or size is.
As per Gauss's law, $\phi=\int \overrightarrow{ E } \cdot \overrightarrow{ dS }=\frac{\sum q}{\varepsilon_0}$
(ii) The term q on the right side of Gauss's law, Eq. (1), includes the sum of all charges enclosed by the surface. The charges may be located anywhere inside the surface.
(iii) In the situation when the surface is so chosen that there are some charges inside and some outside, the electric field [whose flux appears on the left side of Eq. (1)] is due to all the charges, both inside and outside S . The term q on the right side of Gauss's law, however, represents only the total charge inside S .
(iv) The surface that we choose for the application of Gauss's law is called the Gaussian surface. You may choose any Gaussian surface and apply Gauss's law.
(v) Gauss's law is often useful towards a much easier calculation of the electrostatic field when the system has some symmetry. This is facilitated by the choice of a suitable Gaussian surface.
(vi) Finally, Gauss's law is based on the inverse square dependence on distance contained in the Coulomb's law.
As per Gauss's law, $\phi=\int \overrightarrow{ E } \cdot \overrightarrow{ dS }=\frac{\sum q}{\varepsilon_0}$
(ii) The term q on the right side of Gauss's law, Eq. (1), includes the sum of all charges enclosed by the surface. The charges may be located anywhere inside the surface.
(iii) In the situation when the surface is so chosen that there are some charges inside and some outside, the electric field [whose flux appears on the left side of Eq. (1)] is due to all the charges, both inside and outside S . The term q on the right side of Gauss's law, however, represents only the total charge inside S .
(iv) The surface that we choose for the application of Gauss's law is called the Gaussian surface. You may choose any Gaussian surface and apply Gauss's law.
(v) Gauss's law is often useful towards a much easier calculation of the electrostatic field when the system has some symmetry. This is facilitated by the choice of a suitable Gaussian surface.
(vi) Finally, Gauss's law is based on the inverse square dependence on distance contained in the Coulomb's law.
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