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Continuity equation
$$\oint\overrightarrow{E}\cdot\overrightarrow{dl} = q$$ where: oint represents the integration over a closed path. E is the electric field vector...
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$$\oint\overrightarrow{E}\cdot\overrightarrow{dl} = q$$ where: oint represents the integration over a closed path. E is the electric field vector...
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where:
oint represents the integration over a closed path.
E is the electric field vector.
dl is the differential length vector along the path.
q is the charge enclosed by the path.
Interpretation:
The continuity equation tells us that the net flux (the amount of electric field flowing through a closed path) is equal to the charge enclosed by that path. This means that the total charge inside a closed loop must be equal to the total charge outside the loop for the electric field to be continuous throughout the loop.
Implications:
The continuity equation is a fundamental property of electromagnetism and is used to derive many other equations, such as the electric field intensity equation.
It implies that the electric field lines must be continuous, meaning they cannot have sharp corners or breaks.
A violation of the continuity equation would indicate a break in the electric field lines, which could lead to a breakdown in the electrical system.
Examples:
For a constant electric field, the flux is independent of the path, and the equation simplifies to E = q/A, where A is the cross-sectional area of the loop.
For a point charge, the electric field lines form a sphere around the charge, and the flux is equal to the charge itself.
For a uniform electric field in a parallel plate capacitor, the electric field lines are constant and parallel to the plates, and the flux is equal to the charge divided by the area of the plates