Maxwell’s equations describe the behaviour of electric fields and magnetic fields; a more detailed introduction appears in post 25.12. Equations (1)-(4) (highlighted above) are Maxwell’s equations in vector notation. Here E is an electric field, B is a magnetic field, ∇ is the vector operator del, q is charge, ε0 is the permittivity of free… Continue reading 26.6 Maxwell’s equations and electromagnetic waves
This post is a sequel to post 26.4 so I suggest you read that first. In post 26.4, I expressed the Maxwell-Ampère law in terms of two definite integrals. In this post I am going to express it in a differential form. This is similar to what I did in post 25.12 where I expressed… Continue reading 26.5 Differential form of the Maxwell-Ampère law
This is a sequel to post 26.03, so I suggest you read that first. Maxwell realised that Ampère’s law applied only when an electric current, in a conductor enclosed by a magnetic field loop, was constant. If the current changes, for any reason, in the first picture of post 26.03, then equation 1 (of post… Continue reading 26.4 Maxwell-Ampère law
Ampère’s law considers the electric current, I, enclosed by a magnetic field, B, that forms a closed loop. In post 25.16, we saw how to calculate the magnetic field surrounding an electrical current using the Biot-Savart law. Now we are going to consider the current enclosed by a magnetic field line. We will represent an… Continue reading 26.3 Ampère’s law
In post 18.6, I defined a simple harmonic oscillator as a system that was constantly exchanging potential energy and kinetic energy while conserving their sum. I then used the idea of a simple pendulum as an example to illustrate how this works. In post 21.1, I showed how these ideas worked for an electrical simple… Continue reading 26.2 More about the simple harmonic oscillator
I have read several articles about the increasing number of English parents who pay to send their children to private schools and then pay extra for private tuition to gain them a place at Oxford or Cambridge universities (often referred to collectively as Oxbridge); failing that, they hope they will gain a place at one… Continue reading 26.1 Universities where British Nobel Prize-Winners gained their first degree
In post 25.10, I defined the magnetic field, B, caused by an electric current, I1, in a long straight wire, at a point given by a vector r, perpendicular to the wire, by where μ is the permeability of the stuff surrounding the wire, and i × r is the cross product of a unit… Continue reading 25.17 Force on a current in a magnetic field
In post 25.10, I used a special case of the Biot-Savart law to define magnetic field. This law is named after the French physicists Jean-Baptiste Biot (1774-1862) and Félix Savart (1791-1841). But in post 25.15, I described how magnets were known long before Biot and Savart were born. Since magnets attract ferromagnetic material, they must… Continue reading 25.16 Biot-Savart law
So far, in this blog, I have explained that magnetic fields are a result of an electric current (see posts 16.25 and 25.10). But that is not how they were discovered. The idea of a magnetic field came from the properties of permanent magnets (we usually call them simply magnets). A permanent magnet attracts some… Continue reading 25.15 Magnets
Before you read this, I suggest you read post 25.13. Electromagnetic induction arises when a current flows in a circuit when it is in a changing magnetic field (post 25.13). Faraday considered that the current flowed because an induced voltage caused charges in the circuit to move. Moving charges are an electrical current (post 17.44).… Continue reading 25.14 Electromagnetic induction and fields
Thinking about Science with David Hukins 