Measuring c with an LC Circuit

Abstract

Maxwell's discovery of the relation between electricity, magnetism, and light was one of the most important ones in physics. With his added displacement current term, Maxwell showed that the equations of electricity and magnetism produced a radiation solution, electromagnetic (EM) radiation, that traveled with a speed of c=1/ε0μ0. The constant ε0 is the permittivity of free space from electrostatics, and μ0 is the permeability of free space from the magnetic interaction. There are a number of classroom experiments that directly measure the speed of light1–3 and EM radiation4 by dividing distance traveled by time. It is also possible to measure c using standing waves in a microwave oven.5 These are excellent experiments, but do not demonstrate the relationship between c, ε0, and μ0. One can also measure the permittivity of substances in the classroom;6 however, the quantity that is relevant for the speed of EM radiation is the product of ε0 μ0. The product ε0 μ0 is interesting since its units are time2/length2, and its value is the same for any choice of charge units. We present an experiment for the student laboratory to measure this product.