Which 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.

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SSC CGL 2024 Tier-II Official Paper-I (Held On: 18 Jan, 2025)
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  1. Only Statement 2
  2. Neither Statement 1 nor 2
  3. Both Statements 1 and 2
  4. Only Statement 1

Answer (Detailed Solution Below)

Option 4 : Only Statement 1
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Detailed Solution

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The 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.
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