A massless square loop, of wire of resistance $$10 \Omega$$, supporting a mass of $$1 \mathrm{~g}$$, hangs vertically with one of its sides in a uniform magnetic field of $$10^{3} \mathrm{G}$$, directed outwards in the shaded region. A dc voltage $$\mathrm{V}$$ is applied to the loop. For what value of $$\mathrm{V}$$, the magnetic force will exactly balance the weight of the supporting mass of $$1 \mathrm{~g}$$ ?

(If sides of the loop $$=10 \mathrm{~cm}, \mathrm{~g}=10 \mathrm{~ms}^{-2}$$)

The magnetic moments associated with two closely wound circular coils $$\mathrm{A}$$ and $$\mathrm{B}$$ of radius $$\mathrm{r}_{\mathrm{A}}=10$$ $$\mathrm{cm}$$ and $$\mathrm{r}_{\mathrm{B}}=20 \mathrm{~cm}$$ respectively are equal if : (Where $$\mathrm{N}_{\mathrm{A}}, \mathrm{I}_{\mathrm{A}}$$ and $$\mathrm{N}_{\mathrm{B}}, \mathrm{I}_{\mathrm{B}}$$ are number of turn and current of $$\mathrm{A}$$ and $$\mathrm{B}$$ respectively)

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

The magnitude of magnetic induction at mid point $$\mathrm{O}$$ due to current arrangement as shown in Fig will be