Establish the relation, \(\nabla \times H = J + \frac{\partial D}{\partial t}\) where symbols have their usual meanings
Understand the Problem
The question asks to establish the relation (\nabla \times H = J + \frac{\partial D}{\partial t}), where the symbols have their usual meanings. This involves demonstrating how the curl of the magnetic field intensity (H) relates to the current density (J) and the time rate of change of the electric displacement field (D). This equation is one of Maxwell's equations, specifically Ampère's Law with Maxwell's addition.
Answer
The equation is the differential form of Ampère-Maxwell's Law, relating magnetic field intensity, current density, and displacement current density.
The equation (\nabla \times H = J + \frac{\partial D}{\partial t}) represents the differential form of Ampère-Maxwell's Law, where: (\nabla \times H) is the curl of the magnetic field intensity, (J) is the current density, and (\frac{\partial D}{\partial t}) is the displacement current density.
Answer for screen readers
The equation (\nabla \times H = J + \frac{\partial D}{\partial t}) represents the differential form of Ampère-Maxwell's Law, where: (\nabla \times H) is the curl of the magnetic field intensity, (J) is the current density, and (\frac{\partial D}{\partial t}) is the displacement current density.
More Information
This equation is one of Maxwell's equations, fundamental to electromagnetism. It modifies Ampère's circuital law by adding the displacement current term, which is crucial for explaining electromagnetic wave propagation.
Tips
Students sometimes forget the displacement current term (\frac{\partial D}{\partial t}), which is important in dynamic fields.
Sources
- Ampères law: Getting $\nabla \times \vec H = \vec J_{free} + \frac ... - physics.stackexchange.com
- Maxwell's equations - Wikipedia - en.wikipedia.org
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