Both are always there if the circuit is running. Also, both E and M fields are required to transport any power using electricity. This is also true for DC curr

Both are always there if the circuit is running. Also, both E and M fields are required to transport any power using electricity. This is also true for DC current. See https://en.wikipedia.org/wiki/Poynting_vector https://en.wikipedia.org/wiki/Poynting_vector - the formula multiplies E by B, therefore if any of the two is zero no power (or information) transmission can occur. This is true over the air, as well as over a wire.