An oscillating dipole with a large enough dipole moment would cause the bulb to light up. If the resistor is just a resistor with short conductive leads on each end then what happens is the original dipole induces an induced oscillating dipole moment in the resistor. This induce dipole moment results in an electric field pointing into the resistor, a voltage across the resistor, B field lines around the resistor and current through the resistor. All of the above results in the resistor lighting up if it’s a bulb.
The oscillating dipole acts like an emitting antenna, and the resistor a receiving antenna. Obviously the power transfer coefficient will be super super low and geometry dependent. But, for any geometry the transfer coefficient will technically be non zero. So if you use insane amounts of energy radiated by the dipole it will light up the bulb.
The key insight of the Veritasium video that no one seems to explicitly be pointing out is as follows: Under certain conditions, the lumped circuit model for circuits breaks down. If you look at Veritasium's circuit then it is clear the lumped elements are:
- The battery
- The bulb
- The switch
- The wire between the battery and switch, the wire between the battery and bulb and the wire between the switch and the bulb.
If you just look at this circuit on paper you would expect the bulb to light up instantaneously, no matter the size of the wires. The circuit schematic only encodes information about what lumped elements appear in the circuit and their topology. It does not encode any geometric information about the circuit. The point of the Veritasium video is to show that, under certain conditions, geometry is important to accurately predict circuit behavior.
The example in the Veritasium video is contrived, but these exact same physical principles become critically important at higher frequencies and for more sensitive circuits. For example, it a physics lab, you could imagine a 10 A current supply switching on and inducing a 10 mV or more noise voltage on a nearby sensitive photodetector detection line. This level of noise could be problematic for certain applications. The physical principles are the exact same for the two scenarios.
The effect can be explained either by (1) saying the lumped circuit model fails for certain geometric circuits OR (2) saying that a full model of the circuit requires the inclusion of additional, non-obvious, lumped elements such as distributed capacitors and inductors between and along wires.