# Questions tagged [vector-fields]

Vector-fields are vector valued functions which define a vector at each point in space. Examples of the vector field include the electric field and the velocity of a fluid.

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### The flux of a vector field

This is probably a basic question. I'm actually taking a class that introduces me to Maxwell's equations. I am currently trying to make sense of the Gauss's law and have some difficulty understanding ...
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### How does vectorization affect $\nabla$?

The homework and exercise was to prove $\nabla \times {A}$ transform as a vector, and I've solved it thorough hard algebra. However, something occurred to my mind and I have a hard time to resolve it....
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$$\ \\1/2\left( \nabla\mathbf{u} + (\nabla\mathbf{u}) ^\mathrm{T} \right) \$$ Why is the strain rate tensor the equation above?
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### Why do my books introduce the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$ without showing partial derivatives of $\mathbf{E}$ exist?
In electromagnetism (electrostatics), we often come across the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$. In order for this equation to be meaningful, $\mathbf{E}$ must be a ...
For incompressible flow, $$\nabla\cdot \mathbf v=0.$$ That means $\mathbf v$ got to be the gradient of some scalar field. How can I find the scalar field? Is it physically important?