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
I have written about the discovery of electromagnetic induction by Faraday in post 18.21. This earlier post was about inductance in an electrical circuit. Now I want to concentrate on the phenomenon of induction itself. Like Heaviside, Faraday had never attended university but made many important discoveries in chemistry and physics working at the Royal… Continue reading 25.13 Electromagnetic induction
Before you read this, I suggest you read posts 25.9 and 25.11 In 1865, the Scottish physicist Maxwell published a series of differential equations that described the properties of electromagnetic fields. But he had published several previous papers on the subject while he was developing his ideas. Maxwell derived over 20 equations to express his… Continue reading 25.12 Differential form of Gauss’s law
Before you read this, I suggest you read posts 25.9 and 25.10. Gauss’s law is a statement about the electric and magnetic flux in a defined volume of space. It is named after the German physicist and mathematician Carl Gauss (1777-1855). But a lot of other topics in mathematics and physics are named after him,… Continue reading 25.11 Gauss’s law
Before you read this, I suggest you read post 25.9 I introduced the idea of a magnetic field in post 16.25 before I had written about vectors; I am returning to the topic now because I have written more about fields (posts 17.24 and 25.9) and about vectors (posts 17.2 and 17.3). A magnetic field… Continue reading 25.10 Magnetic fields
Before you read this, I suggest you read post 17.24. In posts 16.25 and 17.24 I introduced the idea of a field as a region in space where something experiences force without being directly contacted by an object. In post 19.9 we saw that an electromagnetic wave is an electric and magnetic field that varies… Continue reading 25.9 More about fields: field lines and flux
The purpose of this post is to introduce three properties of the sphere that I hope to use in future posts. A sphere has a constant radius, R. The three properties that I want to explain are The first might be difficult to understand – how can a line be perpendicular to a curved surface?… Continue reading 25.8 The sphere: tangent plane, surface area and volume
Thinking about Science with David Hukins 