Soru
5. Write the differential and integral forms of the fundamental postulates of electrostatics in free space. system after each charge is positions.
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4.4
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Usta · 5 yıl öğretmeni
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Cevap
The differential and integral forms of the fundamental postulates of electrostatics in free space are:Differential Form:1. Gauss's Law: The total electric flux through a closed Gaussian surface is proportional to the total charge enclosed by the surface. Mathematically, it is represented as:∇⋅E = (1/ε₀)∑qenclosedwhere E is the electric field, ε₀ is the permittivity of free space, and qenclosed is the total charge enclosed by the Gaussian surface.2. Faraday's Law of Induction: The rate of change of the magnetic flux through a closed loop is equal to the negative rate of change of the electric potential around the loop. Mathematically, it is represented as:−∂ΦB/∂t = ∂V/∂twhere ΦB is the magnetic flux, V is the electric potential, and t is time.Integral Form:1. Gauss's Law: The total electric flux through a closed Gaussian surface is equal to the total charge enclosed by the surface divided by the permittivity of free space. Mathematically, it is represented as:∫∫∫E⋅dA = (1/ε₀)∑qenclosedwhere E is the electric field, ε₀ is the permittivity of free space, and qenclosed is the total charge enclosed by the Gaussian surface.2. Faraday's Law of Induction: The induced electric potential around a closed loop is equal to the negative rate of change of the magnetic flux through the loop. Mathematically, it is represented as:∫∫∫(−∂ΦB/∂t)⋅dA = ∫∫∫(−∂V/∂t)⋅dAwhere ΦB is the magnetic flux, V is the electric potential, and t is time.