When a galvanometer is shunted by a resistance 'S', its current capacity increases 'n' times. If the same galvanometer is shunted by another resistance '$S^1$', its current capacity will increase to '$n^1$'. The value of n in terms of $n^1$, S and $S^1$ is

A current carrying circular coil of radius 'R' produces magnetic field $B_1$ at an axial point P at a distance 'x' from its centre and $B_2$ at point Q placed at its centre respectively . If $B_2 = 8B_1$, the value of x is

The magnetic induction produced inside an ideal solenoid, depends on which of the following quantities ?
(a) number of turns per unit length.
(b) radius of the wire.
(c) current flowing throught it.
(d) permeability of the medium.

Two circular coils X (smaller) and Y (bigger), each having a single turn, carry equal currents in the same direction and subtend the same angle at point 'O' along the axis of the coil. The distances of the centers of coil to point 'O' are $d$ and $\left(\dfrac{d}{2}\right)$ for coil Y and X respectively. The radii of coils Y and X are $(2r)$ and $(r)$ respectively. The magnetic induction due to the bigger coil at point 'O' is $B_y$ and that due to smaller coil X at point 'O' is $B_x$. ($d \gg r$) The relation between $B_x$ and $B_y$ is