#95🚀 Maxwell's Equations - Trip to California
SuperPowers for Electrical Engineers 🦸🏻♂️🦸🏼♀️
👋 Hello, friends! Dr. Molina here 👨🔧
Welcome to my newsletter! Here, on a weekly basis, I share my personal journey of building a company in the power electronics industry and the exciting new insights I gain about the world of Magnetics.
The Trip to California is about to start
And so it begins...
After three years of preparation, next week marks the start of our American Journey. The suitcases are packed, and even our four-legged companion has received the green light with approved papers 🐕.
This past week in Europe has been filled with a whirlwind of emotions – bidding farewell to family and cherishing memories of our home. However, the anticipation for what lies ahead has us positively thrilled.
We're eagerly looking forward to this significant change, and we've already scheduled meetings and social gatherings in San Francisco for the next two months.
We've been fortunate to receive many beautiful recommendations from kind-hearted folks. Thank you for your invaluable insights!
I'll be sure to keep you posted with updates on our adventures. First on the agenda: buying a car, discovering tennis and pickleball courts, and, of course, finding the best pizza joints in town... you know, the important things 🤣.
Today, I'm excited to share a review of Maxwell's equations with you. Enjoy the read!
Maxwell's Equations
In the process of designing transformers and inductors, Maxwell's equations play a pivotal role. However, up to this point, we haven't delved into them. So, let's take a moment to explore these fundamental equations.
Maxwell's equations are a set of four fundamental equations in electromagnetism that describe the behavior of electric and magnetic fields, as well as their interactions with electric charges and currents. These equations were formulated by James Clerk Maxwell in the 19th century and played a crucial role in unifying the theories of electricity and magnetism.
The four equations are:
Gauss's Law for Electricity
Gauss's Law for Magnetism
Faraday's Law of Electromagnetic Induction
Let’s see what the literature tells us about each equation.
Gauss's Law for Electricity:
This equation relates the electric field (E) to the charge density (ρ). It states that the total electric flux through a closed surface is equal to the charge enclosed by that surface divided by the electric constant (ε₀), also known as the permittivity of free space.
Gauss's Law for Magnetism:
This equation states that the magnetic field (B) does not have any sources (i.e., there are no magnetic monopoles), and the total magnetic flux through any closed surface is always zero.
Faraday's Law of Electromagnetic Induction:
This equation describes how a changing magnetic field induces an electric field (E) around it. It is the basis for understanding electromagnetic induction and the operation of devices like generators and transformers.
This equation relates the circulation of the magnetic field (B) around a closed loop to the total current (J) passing through the loop and the rate of change of the electric field (E) through the loop. Maxwell added the last term to Ampère's original law to account for the role of changing electric fields in generating magnetic fields. In the previous NL, we explained the implications of this law to the Proximity losses.
In these equations:
E represents the electric field vector.
B represents the magnetic field vector.
ρ is the electric charge density.
J is the current density vector.
ε₀ is the electric constant (permittivity of free space).
μ₀ is the magnetic constant (permeability of free space).
∇ is the del operator, which represents the gradient in vector calculus.
∮ represents a closed line integral (circulation) over a closed path.
∫ represents a volume integral over a closed surface.
dl represents an infinitesimal displacement along a closed path.
dA represents an infinitesimal area vector.
Picture source: https://www.pexels.com/es-es/foto/van-naranja-modelo-fundido-a-presion-sobre-pavimento-385997/