Teaching Critical Thinking: An Example From Electricity And Magnetism

As I discussed in this post the other day, I believe that an excellent way to teach critical thinking is to present students with statements that are muddled, garbled, confused, poorly written, or just plain wrong, and instruct them to identify the errors and correct the statements. How can we train students to be critical … Read more

Sense And Nonsense In Elementary Electricity And Magnetism

Today my students wrote the final exam in the first-year university course in electricity and magnetism (+ a two-week introduction to quantum physics at the end of the course) that I taught this past semester. I reproduce the first question on the exam below. Worth 20% of the marks on the exam (each of the … Read more

Carlsberg Beer, Horseshoes, Luck, And Niels Bohr

Niels Bohr was one of the giants of twentieth-century physics. He and Einstein respected each other very much, but their work habits were just about opposite. Einstein preferred to work with just a single assistant, if at all, whereas Bohr worked very hard to secure funding for an institute of theoretical physics in Denmark. Bohr … Read more

Why Radian Measure Makes Life Easier In Mathematics And Physics

The two most commonly used measures for angles are degrees and radians. There are 360 degrees in a full circle (a right angle is 90 degrees), and $2\pi$ radians in a full circle (there are $\pi/2$ radians in a right angle), so there are about 57 degrees in a radian. Students typically learn about degrees … Read more

Is Lenz’s Law Just An Instance Of Newton’s Third Law?

The short answer is, “Yes.” The longer answer exemplifies one of the lovely things about physics: its internal unity, and the fact that a few basic principles manifest in a plethora of circumstances. And one of the typical shortcomings of our textbooks (and by extension our lectures). For me, this was one of the attractions … Read more

Does Nature “Obey” The Laws of Physics?

Today I’d like to discuss a pet peeve of mine. In many physics textbooks, one reads phrases such as: a certain physical system obeys a certain law of physics Here’s an example taken from page 147 of Chemical Principles, by Steven S. Zumdahl, Cengage, 2009 (although I am not trying to single out this author … Read more

Mysteries of Magnetism

The ancient Greeks thought of atoms as the smallest, indivisible bits of matter. By the twentieth century, experiments showed that (what we nowadays call) atoms have internal structure; a key early experiment was the Geiger-Marsden experiment, performed under the supervision of Rutherford, about which we’ll have more to say in a future post. But the … Read more

Atoms in Mathematics and Science; The Concept of a Basis

One of the most important tools that mathematicians and scientists use to cope with the daunting complexity of the world goes by the name of reductionism. That is, one first identifies the key parts of a complex system, then one strives to understand the parts, and finally one strives to understand how the parts fit … Read more

Galileo’s Birthday

Today is Galileo’s birthday, and it’s worth pausing for a moment to celebrate one of the founders of modern science, and one of the giants of its history. The standard biographies of Galileo are by the late Stillman Drake, one of the world’s greatest authorities on Galileo and his life (see here, here, and here). … Read more