Deriving the curl of the magnetic field

Thread starter pkjag
Start date Jan 11, 2014
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Curl deriving Field Magnetic Magnetic field

In summary, the curl of the magnetic field is a vector quantity that represents the direction and magnitude of rotation of the magnetic field around a given point. It is important to derive the curl in order to understand and predict the behavior of magnetic fields in different situations. The curl is calculated using a mathematical operation called the curl operator, which involves taking partial derivatives and combining them in a specific way. Real-world applications of the curl include studying electromagnetism, astrophysics, and engineering. However, there are limitations to deriving the curl, as it assumes a steady-state and does not account for the effects of electric currents.

Jan 11, 2014

pkjag

So i was wondering how the curl of the magnetic field is derived since Feynman just introduces it from nothing in his second volume of Feynman's lectures on physics:

c²∇xB=j/ε₀

or the other one where ∇x B=μ₀j

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Jan 11, 2014

dextercioby

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Do you know about the Biot-Savart's law and how to pass mathematically from one type of integral to another (Stokes formulas) ?

Related to Deriving the curl of the magnetic field

1. What is the curl of the magnetic field?

The curl of the magnetic field is a measure of how much the magnetic field is rotating or circulating around a given point. It is a vector quantity that represents the direction and magnitude of the rotation.

2. Why is it important to derive the curl of the magnetic field?

Deriving the curl of the magnetic field allows us to understand and analyze the behavior of magnetic fields in various situations. It helps us to predict how the magnetic field will change over time and how it interacts with other fields and particles.

3. How is the curl of the magnetic field calculated?

The curl of the magnetic field is calculated using a mathematical operation called the curl operator. This involves taking the partial derivatives of the magnetic field components with respect to each coordinate axis and then combining them in a specific way to obtain the curl vector.

4. What are some real-world applications of the curl of the magnetic field?

The curl of the magnetic field is used extensively in the fields of electromagnetism, astrophysics, and engineering. It is used to study the behavior of magnetic fields in motors, generators, and other devices. It also helps us understand phenomena such as the Earth's magnetic field and the formation of stars and galaxies.

5. Are there any limitations to deriving the curl of the magnetic field?

While deriving the curl of the magnetic field is a useful tool in understanding magnetic fields, it does have some limitations. It assumes a steady-state, meaning that it does not take into account time-varying fields. It also does not account for the effects of electric currents, which can influence the magnetic field in some situations.