To know the resistance G of a galvanometer by half deflection method, a battery of emf V_E and resistance R is used to deflect the galvanometer by angle $$\theta $$. If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation :

Two identical wires $$A$$ and $$B,$$ each of length $$'l'$$, carry the same current $$I$$. Wire $$A$$ is bent into a circle of radius $$R$$ and wire $$B$$ is bent to form a square of side $$'a'$$. If $${B_A}$$ and $${B_B}$$ are the values of magnetic fields at the centres of the circle and square respectively, then the ratio $${{{B_A}} \over {{B_B}}}$$ is:

Two long current carrying thin wires, both with current $$I,$$ are held by insulating threads of length $$L$$ and are in equilibrium as shown in the figure, with threads making an angle $$'\theta '$$ with the vertical. If wires have mass $$\lambda $$ per unit-length then the value of $$I$$ is :
($$g=$$ $$gravitational$$ $$acceleration$$ )

A rectangular loop of sides $$10$$ $$cm$$ and $$5$$ $$cm$$ carrying a current $$1$$ of $$12A$$ is placed in different orientations as shown in the figures below :

If there is a uniform magnetic field of $$0.3$$ $$T$$ in the positive $$z$$ direction, in which orientations the loop would be in $$(i)$$ stable equilibrium and $$(ii)$$ unstable equilibrium ?