Electronics Engineering (ELEX) Board Practice Exam

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Which of the following represents Maxwell's first equation in free space?

▽•D = ρ
▽×E = -∂B/∂t
▽×H = D
▽•B = 0

The correct answer is: ▽×H = D

Maxwell's first equation in free space is often identified as Gauss's law for electric fields, which is represented in differential form. However, the correct representation indicating that there are no free charges in the region (meaning that the electric displacement field is divergence-free in free space) is given by ∇•D = ρ, where D is the electric displacement field and ρ is the charge density. In free space, with no free charges present, this equation simplifies, and ∇•D becomes zero. The correct representation of Maxwell's first equation in free space, when adjusted for context, aligns more closely with Gauss's law for magnetic fields, which states that the divergence of the magnetic field B is zero, indicating there are no magnetic monopoles. The other options listed refer to different aspects of Maxwell's equations: - The option regarding the curl of E being equal to the negative rate of change of B relates to Faraday's law of induction. - The option suggesting the curl of H being equal to D pertains to Ampère's circuital law with Maxwell's correction. - The option about the divergence of B being zero highlights the absence of magnetic monopoles, which directly associates with the magnetic field aspects rather than electric fields.