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Questions and Answers
What does the integral form of Gauss’s law state?
What does the integral form of Gauss’s law state?
- $ abla oldsymbol{ abla} imes extbf{E} = rac{Q}{ extbf{ε}_{0}}$
- $ abla oldsymbol{ abla} imes extbf{E} = 4 extbf{π}ρ$
- $ abla oldsymbol{ abla} imes extbf{E} = rac{Q}{ extbf{ε}_{0}} + rac{ extbf{ε}_{0}}{Q}$
- $ abla oldsymbol{ abla} imes extbf{E} = rac{Q}{ extbf{ε}_{0}}$
What does Gauss’s law for the electric field describe?
What does Gauss’s law for the electric field describe?
- The magnetic field generated by a distribution of electric charges
- The gravitational field generated by a distribution of electric charges
- The static electric field generated by a distribution of electric charges (correct)
- The dynamic electric field generated by a distribution of electric charges
What does a positive electric charge generate according to convention?
What does a positive electric charge generate according to convention?
- A magnetic field
- No electric field
- A positive electric field (correct)
- A negative electric field
When was Gauss’s law for the electric field published?
When was Gauss’s law for the electric field published?
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What is the electric permittivity of free space denoted as in Gauss’s law?
What is the electric permittivity of free space denoted as in Gauss’s law?
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Study Notes
Integral Form of Gauss's Law
- States that the electric flux through a closed surface is proportional to the charge enclosed within that surface.
- Mathematically represented as ∮ E ⋅ dA = Q_enc/ε₀, where E is the electric field, dA is the differential area vector, Q_enc is the enclosed charge, and ε₀ is the electric permittivity of free space.
Gauss's Law for Electric Field
- Describes the relationship between electric charge distribution and the resulting electric field.
- It is particularly useful for calculating electric fields for symmetrical charge distributions.
Positive Electric Charge Convention
- According to convention, a positive electric charge generates an outward electric field.
- Electric field lines emanate from positive charges and terminate on negative charges, indicating the direction of force on a positive test charge.
Publication of Gauss's Law
- Gauss's law for the electric field was published in 1835.
- Named after mathematician and physicist Carl Friedrich Gauss, who contributed significantly to the field of electrostatics.
Electric Permittivity of Free Space
- Denoted as ε₀ in Gauss's law.
- Represents the capability of a vacuum to permit electric field lines and is a fundamental constant in electromagnetism, with a value of approximately 8.85 x 10⁻¹² F/m.
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