Question
Download Solution PDFWhich of the following statements is/are correct?
Statements:
1) Ampere's Law describes the relationship between electric current and the magnetic field it produces.
2) Maxwell's equations are a set of four fundamental equations governing electric and magnetic fields in the absence of charges and currents.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is Option 4.
Key Points
- Ampere's Law describes the relationship between electric current and the magnetic field it produces.
- According to Ampere's Law, the magnetic field in space around an electric current is proportional to the electric current which serves as its source.
- Ampere’s Law is mathematically expressed as ∮B·dl = μ₀I, where B is the magnetic field, dl is a differential element of the path, μ₀ is the permeability of free space, and I is the current enclosed by the path.
- Maxwell's equations govern electric and magnetic fields, but they also account for the presence of charges and currents, not just their absence.
Additional Information
- Maxwell's Equations
- Maxwell's equations consist of four fundamental laws: Gauss's law, Gauss's law for magnetism, Faraday's law of induction, and Ampere's law (with Maxwell's addition).
- These equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields.
- In the presence of charges and currents, Maxwell's equations provide a complete set of rules for the behavior of electric and magnetic fields.
- Gauss's Law
- Gauss's Law states that the electric flux through a closed surface is proportional to the charge enclosed by the surface.
- Mathematically, it is expressed as ∮E·dA = Q/ε₀, where E is the electric field, dA is a differential area on the closed surface, Q is the total charge enclosed, and ε₀ is the permittivity of free space.
- Faraday's Law of Induction
- Faraday's Law of Induction states that a change in magnetic field within a closed loop induces an electromotive force (EMF) in the wire loop.
- This is mathematically represented as ε = -dΦB/dt, where ε is the induced EMF and ΦB is the magnetic flux.
- Permeability and Permittivity
- The permeability of free space (μ₀) is a constant that characterizes the ability of a material to support the formation of a magnetic field within itself.
- The permittivity of free space (ε₀) is a constant that characterizes the ability of a material to transmit an electric field within itself.
Last updated on Jul 9, 2025
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