# Time Varying Magnetic Field

What is said time varying magnetic field? I have heard a lot about it and the Internet is not willing to give me any answers. I assume time varying is a qualification, I was reading around here and heard about an induced magnetic field so I take it that is another qualification? What does that mean? Thank you.

• Uhhh...a time varying magnetic field is a magnetic field that varies with time? What are you asking? Commented Jul 2, 2014 at 13:10
• @ACuriousMind Precisely. I just want a more specific answer. Commented Jul 2, 2014 at 14:04

Time-varying means that as time, $t$, increases, the magnetic field changes. One of the more common representations is a sinusoidal wave:

(image from the linked Wikipedia page). Though the image above says $x$, the relation between $x$ and $\sin(x)$ is what is important.

With magnetic fields, Maxwell's equations, $$\nabla\cdot\mathbf E=\frac\rho{\epsilon_0} \quad \nabla\cdot\mathbf B=0 \\ \nabla\times\mathbf E=0 \quad \nabla\times\mathbf B=\mu_0\mathbf J$$ (where $\mathbf E$ is the electric field, $\mathbf B$ the magnetic field, $\mathbf J$ the current density, $\epsilon_0$ the vacuum permittivity, $\rho$ the charge density, and $\mu_0$ the vacuum permeability) then become $$\nabla\cdot\mathbf E=\frac\rho{\epsilon_0} \quad \nabla\cdot\mathbf B=0 \\ \nabla\times\mathbf E=\color{blue}{-\frac{\partial\mathbf B}{\partial t}} \quad \nabla\times\mathbf B=\mu_0\mathbf J+\color{blue}{\frac{1}{c^2}\frac{\partial\mathbf E}{\partial t}}$$ where the blue-colored terms show that the two fields induce each other when changing in space and/or time.

Time varying magnetic field $\vec{B}(t)$ or any quantity. It means which varies with time.

Let us understand by an example:

$\vec{B}(t) = B_{0}f(t)\hat{B}$.

It means that, $f(t)$ is different from a time $t_2$ which is either before or after $t_1$, if $t_1$ and $t_2$ are distinct. This changing behaviour may arise because of some external regulations.

My simultaneous use before and after is showing that in either case quantity is different.

• What is $\hat{B}$? Commented Jul 2, 2014 at 13:41
• @KyleKanos, Direction of $\vec{B}$ denoting it by a unit vector.
– L.K.
Commented Jul 2, 2014 at 13:46