My gut feeling is that the question originates from a mental model of a world full of physical bodies, i.e. things. A drawing in this world depicts a physical object: A chair, a table, a house. Planets. I can manipulate the smaller ones: Take them elsewhere, turn them over. The bigger ones influence each other: The sun attracts the planets which orbit around it.

I can only draw things which exist, in this palpable sense.

Now somebody draws a magnetic field. I interpret your question in this sense: Does this drawing depict something that really, physically, bodily exists? The answer, unfortunately, goes in the opposite direction of what your question implies. The physical objects we see are actually systems of fields. The chair is a collection of nuclei held in place by electrostatic and -dynamic interaction between charged particles; and on a closer look we cannot maintain the "bodily existence" of any particles in a solid body sense. They are waves, quantum states, probabilities, processes, which in the particular case of the chair I'm sitting in right now congeal to an overwhelmingly probable interaction with my behind resting on it.

The answer therefore is that a magnetic field like the earth's is exactly as real as anything else around you; not more, and not less. But the reason is that the air of "reality" our daily surroundings emanate is rather deceiving.

My gut feeling is that the question originates from a mental model of a world full of physical bodies, i.e. things. A drawing in this world depicts a physical object: A chair, a table, a house. Planets. I can manipulate the smaller ones: Take them elsewhere, turn them over. The bigger ones influence each other: The sun attracts the planets which orbit around it.

I can only draw things which exist, in this palpable sense.

Now somebody draws a magnetic field. I interpret your question in this sense: Does this drawing depict something that really, physically, bodily exists? The answer, unfortunately, goes in the opposite direction of what your question implies. The physical objects we see are actually systems of fields. The chair is a collection of nuclei and electrons held in place by electrostatic and -dynamic interaction; and on a closer look we cannot maintain the "bodily existence" of any of these "particles" in any "solid-matter" sense. They are waves, quantum states, probabilities, processes, which in the particular case of the chair I'm sitting in right now congeal to an overwhelmingly probable interaction with my behind resting on it. Phew.

The answer therefore is that a magnetic field like the earth's is exactly as real as anything else around you; not more, and not less. But the reason is that the air of "reality" our daily surroundings emanate is rather deceiving.