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Maxwell's Equations are a set of 4 equations that describe how electric and magnetic fields behave within our universe, as well as how they interact with each other. In this video, we look at each of the terms found in these equations. #maxwell #electromagnetism #fields
The first equation (Gauss' Law for Magnetism) states that the divergence of the magnetic field is equal to zero. In other words, it describes how any magnetic field must behave in order to exist in our universe. A magnetic field is a vector field that describes the forces exerted on external magnets placed in the field. The direction shows the direction of the force exerted on the north pole of the external magnet, while the size shows the strength of the force.
The divergence of this field (calculated using the vector operator nabla), can be geometrically interpreted as the amount of field flowing out minus the amount of field flowing in. Since the divergence is zero, this means all magnetic fields must flow in and flow at at exactly the same rate out of any closed volume we may choose.
The second equation (Gauss' Law for Electricity) states that the divergence of the electric field is equal to the charge density in a given region of space divided by the permittivity of free space (electric constant). An electric field shows the forces exerted on a positive external charge placed in the field. And the divergence of this can be nonzero.
This divergence depends on the density of charge found within the considered volume of space. The larger the charge density, the larger the divergence. And the sign of the charges determines the sign of the divergence of course.
The permittivity of free space is a constant that determines how strong an electric field can be generated by a given charged object within our universe.
The third Maxwell equation (Maxwell-Faraday Equation) states that the curl of an electric field can be found by calculating the rate of change of any magnetic field in our system. In other words, a changing magnetic field can generate an electric field. The curl operator can be thought of as measuring the "circulation" of the field, which we discuss in this video.
The final Maxwell equation (Ampere's Circuital Law) states that the curl of the magnetic field can be found by calculating the rate of change of an electric field, as well as by calculating the displacement current, with some factor of the permeability of free space also included.
The permeability of free space is a constant that determines how strong a magnetic field can be generated by a given magnet within our universe.
The displacement current is a term Maxwell added to an equation that already existed, but was incomplete. It basically refers to the net charge flowing in or out of the region of space we are considering - hence a current. A magnetic field can be generated by changing the electric field within the region of space, or due to a flow of current in or out of the space.
All of these equations can be combined to create the electromagnetic wave equation, which describes how EM waves move through a vacuum at the speed of light. Also, the speed of light is directly related to both the permittivity, and the permeability of free space.
Here are some useful links.
My Maxwell's Equations playlist: youtube.com/playlist?list=PLOlz9q28K2e6aNgl1zt1xccyy4Ofl3YAk
My video on the del / nabla operator: youtu.be/hI4yTE8WT88
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Timestamps:
0:00 - The 4 Maxwell Equations
1:03 - Equation 1, Gauss' Law for Magnetism
3:15 - A Word from Wren, Our Sponsor
5:06 - Equation 2, Gauss' Law for Electricity
7:52 - Equation 3, Maxwell-Faraday Equation
10:30 - Equation 4, Ampere's Circuital Law
11:54 - Fun Fact About the Speed of Light!
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