I am running an experiment in which an AC source generating current at 50 Hz is in series with a resistor and am measuring the current and induced magnetic field in air. Should I expect there to be a phase lag between the current and the magnetic field or should they be in phase? I know Biot-Savart's law is $B= \frac{\mu_0 I}{2\pi r}$, and there is no $e^{i\omega t}$ in that equation, so there should be no phase lag, but in my measurment, I'm seeing that the two are 180 degrees out of phase. I thought it might have been because I'm using a differential probe and may have hooked up the probe backwards, but I've double checked and this doesn't seem to be the case.
Below is a circuit diagram of my experiment.
And below is the result I am getting from my measurement on a NI-DAQ USB-6225 differential analog input board. The blue curve corresponds to the voltage coming from the differential probe, which has been converted into magnetic field strength, and the orange curve corresponds to the measurement from the Hall effect sensor.
