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 :

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75^o. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30^o with this field. The magnitude of the other field (in mT ) is close to

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 :
($$g=$$ $$gravitational$$ $$acceleration$$ )