Describe the working principle of a moving coil galvanometer. Why is it necessary to use (i) a radial magnetic field.

The magnitude F of the force between two straight parallel current carrying conductors kept at a distance d apart in air is given by $F=\frac{{\mu }_0}{2\pi }\frac{I_1{I}_2}{d}$, where $I_1$ and $I_2$ are the currents flowing through the two wires. Use this expression, and the sign convention that the: "Force of attraction is assigned a negative sign and force of repulsion is assigned a positive sign". Draw graphs showing dependence of $F$ on

(i) $I_1{I}_2$ when $d$ is kept constant.

The magnitude F of the force between two straight parallel current carrying conductors kept at a distance d apart in air is given by $F=\frac{{\mu }_0}{2\pi }\frac{I_1{I}_2}{d}$, where $I_1$ and $I_2$ are the currents flowing through the two wires. Use this expression, and the sign convention that the: "Force of attraction is assigned a negative sign and force of repulsion is assigned a positive sign". Draw graphs showing dependence of $F$ on

(ii) $d$ when the product $I_1{I}_2$ is maintained at a constant positive value.

The magnitude F of the force between two straight parallel current carrying conductors kept at a distance d apart in air is given by $F=\frac{{\mu }_0}{2\pi }\frac{I_1{I}_2}{d}$, where $I_1$ and $I_2$ are the currents flowing through the two wires. Use this expression, and the sign convention that the: "Force of attraction is assigned a negative sign and force of repulsion is assigned a positive sign". Draw graphs showing dependence of $F$ on

(ii) $d$ when the product $I_1{I}_2$ is maintained at a constant negative value.

The current flowing in the galvanometer $G$ when the key $k_2$ is kept open is $I$. On closing the key $k_2$ , the current in the galvanometer becomes $\raisebox{1ex}{$I$}\!\left/ \!\raisebox{-1ex}{$n$}\right.$, where $n$ is an integer. Obtain an expression for resistance $R_g$ of the galvanometer in terms of $R,S$ and $n$. To what form does this expression reduce when the value of $R$ is very large as compared to $S$ ?