# What does changing electric field induces?

## Question:

What does changing electric field induces?

## Maxwell's Equations:

Maxwell's equations are a set of 4 equations that describe the behavior of electromagnetic waves. Maxwell's equations are considered as some of the most important equations in physics due to the sheer impact they have provided toward the development of our modern electronics and optics. Maxwell's equations include Gauss' law for electric fields, Gauss' law of magnetism, Ampere's law, and Faraday's law of electromagnetic induction.

Faraday's law of electromagnetic induction states that a changing electric field will induce a changing magnetic field. The differential form of Faraday's law can be written as:

{eq}\displaystyle \rm \vec{\nabla}\ \times\ \vec{E} = -\frac{\partial \vec{B}}{\partial t} {/eq}

The integral form can be written as:

{eq}\displaystyle \rm \oint \vec{E}\ \cdot\ d\vec{l} = - \int\ \frac{\partial \vec{B}}{\partial t}\ \cdot\ d\vec{A} {/eq}

The relationship between the electric field {eq}\displaystyle \rm \vec{E} {/eq} and magnetic field {eq}\displaystyle \rm \vec{B} {/eq} gave birth to some of the following concepts:

• Electromotive force - since the integral of an electric field with space is an electric potential, this allowed for the generation of voltages just by changing the magnetic flux (which is the product of the magnetic field and the area of a closed loop conductor) flowing through an object. This concept is used in electrical generators today.
• Propagation of electromagnetic waves - changing electric fields induce changing magnetic fields, and changing magnetic fields, in return, also induce changing electric fields. This discovery led to vast developments in our understanding of electromagnetic waves. 