Why is there no current in the right loop of this circuit?

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Because for any inductor the current is an integral:
[tex]i = \int_{t_0}^{t}\frac{v(t)}{L}\ dt + i(t_0)[/tex]

Immediately after the switch S closes mean that [tex]t = t_0[/tex], so the current is zero.

[tex]i(t_0)[/tex] is zero since before that moment the switch was open.