How does the deflection of a compass increases if a current carrying wire is kept at the same point, but its current is increased?

Question

In my physics book, there is an activity which explains how to draw magnetic field lines (which will be in shape of circles) of a current carrying wire using a compass. Later it says that if we increase the current of the circuit, the deflection of the compass increases.

If I am not wrong then there will be different circles formed which will intersect with the circles drawn earlier. Both circles should have the same centre. But it is not possible for concentric circles to intersect.

Can anyone please explain what I did wrong or if I didn't do anything wrong then how is this concept right?

This is the the chapter of my physics book. You can see pp. 4–5 of the pdf, activity 13.5 and the next paragraph.

Answer 1

You're not entirely wrong here:

If the current was the only magnetic field source, it wouldn't matter how strong or weak the current was, the "deflection" would be the same.

Presumably what they mean here is to consider the combination of the Earth's magnetic field and the current's field. As the current increases, its field dominates the compass' deflection, and as the current decreases the Earth's field dominates. The magnetic field lines from the current alone don't tell the whole story.