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Savant13
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I'm working with Maxwell's equations, and I have found the curl of a magnetic field at all points. How can I figure out what the magnetic field is at those points?
Savant13 said:In this case, the magnetic field is being created by an electric dipole consisting of two point particles of equal mass and opposite charge in mutual orbit, not a current, so the Biot-Savart law doesn't apply
weichi said:Ben is of course correct - there *is* a current here. It would be a good exercise to calculate it! Note that this is, in a sense, a "baby" version of the problem you are asking about, but in this case you need to find a vector field who's *divergence* you know.
But once you calculate the current, Biot-Savart isn't going to help you. Do you see why?
Savant13 said:Is it because the current is not constant?
weichi said:Ben is of course correct - there *is* a current here. It would be a good exercise to calculate it! Note that this is, in a sense, a "baby" version of the problem you are asking about, but in this case you need to find a vector field who's *divergence* you know.
But once you calculate the current, Biot-Savart isn't going to help you. Do you see why?
Savant13 said:I think I know how I can do this.
Is it possible for a vector field to be perpendicular to its divergence at a point?
Maxwell's Equations are a set of four fundamental equations in electromagnetism that describe the relationship between electric and magnetic fields, electric charges, and electric currents.
The "curl" in Maxwell's Equations refers to the mathematical operation that describes the rotation or circulation of a vector field. In the context of electromagnetism, it is used to calculate the magnetic field from the electric field and vice versa.
The magnetic field can be found by taking the curl of the electric field. This operation involves taking the partial derivatives of the electric field with respect to each spatial coordinate and then combining them in a specific way, as described in the curl equation.
The units of the magnetic field in Maxwell's Equations are typically measured in teslas (T) in the SI system. In other systems, it may be measured in gauss (G) or oersteds (Oe).
Maxwell's Equations are used in a wide range of real-world applications, including the design and operation of electrical and electronic devices, telecommunications, and the study of electromagnetic radiation. They are also essential for understanding and predicting the behavior of electromagnetic fields and waves in various systems and environments.