Before you read this, I suggest you read post 26.8. We’re going to think about hypothetical twins. When they become adults, one works in a bank: the other becomes an astronaut. The astronaut goes on a very long journey often at speeds comparable to the speed of light. During this time, the banker twin becomes… Continue reading 26.9 The twin paradox
Before you read this, I suggest you read posts 16.12 and 26.7. I introduced the concept of time in post 16.12. However, the special theory of relativity leads to an unexpected property of time – it depends on the state of motion of an observer; time does not pass equally in different inertial frames of… Continue reading 26.8 Time dilation
In this post, I am returning to the subject of relative motion, that I first described in posts 16.4 and 16.12. But we shall see that this description is complicated by what I wrote in post 26.6. According to post 26.6, the speed, c, of an electromagnetic wave (for example, light), in a vacuum, is… Continue reading 26.7 Einstein’s special theory of relativity
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
