Observation of the Intrinsic Abraham Force in Time-Varying Magnetic and Electric Fields

The Abraham force exerted by a time-dependent electromagnetic field on neutral, polarizable matter has two contributions. The one induced by a time-varying magnetic field and a static electric field is reported here for the first time. We discuss our results in the context of the radiative momentum in matter. Our observations are consistent with Abraham’s and Nelson’s versions for radiative momentum.

Figure 1

Schematic setup of the experiment. A magnetic field $B$ is applied perpendicular to the drawing at frequency ${\omega }_B$, and high voltage at frequency ${\omega }_E$ is applied to the electrodes of the sample. The cantilever signal is phase sensitively detected at the sum frequency ${\omega }_B+{\omega }_E$. Typical sample size is $9\times 2\times 0.35{\mathrm{mm}}^3$. PSD stands for phase sensitive detector.

Figure 2

Abraham force exerted on a slab of Y5V dielectric by crossed oscillating electric and magnetic fields ($f_i={\omega }_i/2\pi$). Straight lines are linear fits to the data.

Figure 3

Dependence of the Abraham force on a solidly contacted Y5V slab on the frequencies of the electric and magnetic fields, while the sum frequency and the amplitudes are kept constant. The solid line is a linear fit to the data. Note that the intercept with the ordinate of the theoretical lines (dashed and dot-dashed, see text) is subject to a systematic uncertainty of 5%.

Figure 4

Section of the $\mathrm{\text{sample}}+\mathrm{\text{contacts}}$, showing the different surface charges.

Figure 5

Modified cantilever setup. Electrodes are fixed to the lab frame, and electrical contact to the sample is provided by an ionic liquid.

Figure 6

Abraham force measured on a Y5V slab, contacted by an ionic liquid as illustrated in Fig. 5. $f_E+f_B=690\mathrm{Hz}$. The solid line is a linear fit to the raw data (closed symbols). The dashed line is a linear fit to the corrected data (see text).