# Electronic – Transformer core radius and number of turns

transformer

I'm trying to solve this question.

For a specified input voltage and frequency, if the equivalent radius
of the core of a transformer is reduced by half, the factor by which
the number of turns in the primary should change to maintain the same

If radius is halved, area becomes $$\ 1/4\$$ times. Hence to maintain the same no load current, there needs to be 4 times the number of turns we had earlier.

But the given answer is 2 times the number of turns. Why is that?

For a closed magnetic core $$\\ell\$$ becomes the mean length around the core.