I thought it’d be good to show my A-Level students how to model an electromagnetic wave using a sinusoidal wave function for the electric and magnetic fields, and how these can be substituted into Maxwell’s Equations to derive the speed of light.
There are a few ways to derive the speed of light from Maxwell’s Equations, such as taking the curl of both sides, but I wanted to use mathematics that was accessible to A-Level students, which meant not going beyond partial derivatives.
I managed to derive the speed of light (see below); however, I needed to do a bit of mathematical ‘sleight-of-hand‘, by ignoring Lenz’s Law (the minus sign in Maxwell’s third equation). I’m not happy with that, so I’ve asked some colleagues on the Isaac Physics WhatsApp group if they can come up with a justification for ignoring Lenz’s Law or, better yet, spot a mistake in my derivation. My working is shown below.
If you spot a mistake or can think of how to justify ignoring Lenz’s Law, please do comment below to let me know! Remember, I want to keep this accessible to A-Level students.
Reminder: Weekly Live Tuition Sessions!
SUNDAY 11th January
GCSE Physics 9:30am – 10:20am Infrared radiation A-Level Physics 10:30am – 11:20am Measurement of specific charge GCSE Astronomy 11:30am – 12:20pm Exploring the moon If you wish to enrol on the tuition sessions and haven’t yet, then click enrol below
Physics with Keith 