The deflections produced by a Tangent Galvanometer at two different...

Tangent galvanometer is& a galvanometer with a very small magnetic needle in the middle of a big vertical circular coil of wire through which electric current is conducted and whose plane is in the magnetic meridian, with the current intensity proportional to the tangent of the needle's angle of deflection.

According to tangent law, the magnetic field when the deflection in needle is& $\theta$,

$B = {B}_{H}tan\theta$

Here,~$B = \dfrac{{μ}_{0}nI}{2r}$

As, the same current is passed through the galvanometer at both the places,~${B}_{H} ∝ \dfrac{1}{tan\theta}$

$⇒ \dfrac{\left({B}_{H}\right)1}{\left({B}_{H}\right)2} = \dfrac{tan{θ}_{2}}{tan{θ}_{1}} = \dfrac{\tan \left(45 °\right)}{\tan \left(60 °\right)} = \dfrac{3}{1}$