Need some confirmation regarding induced currents

[mymodded]

TL;DR Summary: if there are 2 coils, one with a switch and a battery. If the switch is closed, exactly at that moment when the switch is closed, there is no induced voltage in the other coil, am I correct?

In this image, exactly at the moment when we close the switch, there should only be induced voltage in the first coil (left coil), am I right? That's because the coil resists any changes in current so at t = 0, there is no current in the left circuit, thus, there is no change in magnetic flux in the second coil. Am I correct in my reasoning?

I am asking this because there was a question about this, and there was no choice saying that voltage is only induced the first coil.

 

[kuruman]

Please explain what you understand the state of the switch to be when you say "exactly at the moment when we close the switch." Is the switch open or closed at that "exact" moment? It's a binary choice: 0 or 1. Let's explore each choice. We assume that there is some resistance in the coils.

0 = switch open. Nothing has changed. There is no current anywhere and no magnetic field anywhere.

1 = switch closed. The current in the primary coil (on the left) is zero but is increasing. The magnetic field in the primary is proportional to the current, also zero and increasing. In the secondary coil (on the right) the flux from the primary is zero and increasing. (We assume that the coils are close enough to ignore the transit time of the EM signal from the left coil to the right.)

Does this resolve your question?