# Solving Del Cross Question: Why is del x dB/dt = mu dJ/dt?

• miew
In summary, the del operator, also known as del x, is used to represent the gradient of a vector field in the equation del x dB/dt = mu dJ/dt. This equation is important in solving electromagnetic problems as it relates the change in magnetic field to current density and permeability of the medium. Mu represents the permeability of the medium and varies depending on the material being studied. The equation also relates to Faraday's law of induction and the units of measurement for the variables are inverse meters, tesla per second, henrys per meter, and amperes per square meter.
miew

## Homework Statement

I have to do an E&M problem, I think I got it, but I made a few steps that I don't really understand. The first one is:

If delxB= muJ
Does
del x dB/dt = mu dJ/dt ??
If so, why ?

I tried using latex, but it didn't work...sorry :(

## The Attempt at a Solution

hi miew!

(have a del: ∇ and a curly d: ∂ and a mu: µ )

yes, because derivatives wrt independent variables always commute (ie you can always change the order) …

2/∂x∂t = ∂2/∂t∂x

Thanks ! that makes sense :)

## 1. What is the meaning of del x in the equation del x dB/dt = mu dJ/dt?

Del x, also known as the del operator, is a mathematical symbol that represents the gradient of a vector field. In the context of this equation, it is used to represent the spatial derivative of the magnetic field, dB/dt.

## 2. Why is the equation del x dB/dt = mu dJ/dt important in solving electromagnetic problems?

This equation is important because it relates the change in the magnetic field (dB/dt) to the current density (dJ/dt) and the permeability of the medium (mu). It is a fundamental equation in electromagnetics and is used to understand and solve problems related to the behavior of electric and magnetic fields.

## 3. What does the term mu represent in the equation del x dB/dt = mu dJ/dt?

In this equation, mu represents the permeability of the medium, which is a measure of how easily a material can be magnetized. It is a fundamental property of a material and varies depending on the medium in which the electromagnetic problem is being solved.

## 4. How does the equation del x dB/dt = mu dJ/dt relate to Faraday's law of induction?

The equation del x dB/dt = mu dJ/dt is essentially Faraday's law of induction in the time domain. It states that the induced electric field (del x dB/dt) is equal to the negative of the time rate of change of the magnetic flux density (dB/dt) multiplied by the permeability (mu) of the medium.

## 5. What are the units of measurement for the variables in the equation del x dB/dt = mu dJ/dt?

The units of measurement for the variables in this equation are as follows: del x is measured in inverse meters (1/m), dB/dt is measured in tesla per second (T/s), mu is measured in henrys per meter (H/m), and dJ/dt is measured in amperes per square meter (A/m^2).

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