Yes, electric flux can be zero.
According to Gauss's law, the electric flux through a closed surface is directly proportional to the net electric charge enclosed within that surface. This key relationship dictates whether the electric flux is zero or non-zero.
Understanding Electric Flux and Gauss's Law
Electric flux is a measure of the electric field passing through a given surface. Gauss's law provides a powerful tool for calculating electric flux, particularly when dealing with symmetrical charge distributions.
Here's a breakdown:
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Electric Flux (ΦE): Represents the measure of the electric field through a given area.
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Gauss's Law: States that the total electric flux through a closed surface (Gaussian surface) is proportional to the net electric charge enclosed within that surface. Mathematically:
ΦE = Qenc / ε0
Where:
- ΦE is the electric flux.
- Qenc is the net charge enclosed by the Gaussian surface.
- ε0 is the permittivity of free space (a constant).
Conditions for Zero Electric Flux
Based on Gauss's Law and the reference, electric flux (ΦE) becomes zero under the following condition:
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Zero Net Enclosed Charge: When the net charge (Qenc) enclosed by a closed surface is zero, the electric flux through that closed surface is zero.
- This means that if the total positive charge is equal to the total negative charge inside the closed surface, the net charge is zero, and therefore the electric flux is zero.
Examples
Here are a few examples illustrating situations where electric flux is zero:
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A closed surface enclosing an electric dipole: An electric dipole consists of two equal and opposite charges (+q and -q) separated by a small distance. If a Gaussian surface encloses both charges, the net charge enclosed is zero (+q - q = 0), resulting in zero electric flux through the surface.
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A neutral conducting sphere in a uniform electric field: While there is an electric field present, the charges within the conductor redistribute themselves so that the net charge enclosed by any Gaussian surface within the conductor remains zero. Hence, electric flux through the Gaussian surface is zero.
Table Summary: Electric Flux Scenarios
| Scenario | Net Charge Enclosed (Qenc) | Electric Flux (ΦE) |
|---|---|---|
| Non-zero net charge enclosed | Qenc ≠ 0 | ΦE ≠ 0 |
| Zero net charge enclosed | Qenc = 0 | ΦE = 0 |
