Current in secondary of transformer

I am trying to get a better understanding of transformers. Assuming the transformer is ideal, and the secondary is connected to a high impedance load such as an oscilloscope, would there essentially be no current in the secondary?

In this case the turn ratio is one. So ideally, the voltages would be equal. However, if there is no current in the secondary, what is happening to the power that is transferred to the secondary? Does it just remain in the magnetic field? Thanks
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