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

Two thin long parallel wires, $W_1$ and $W_2$ separated by distance '$a$', carry currents $i$ and $3i$ respectively in the same direction. The magnitude of the force per unit length exerted by wire $W_1$ on wire $W_2$ is

A particle of charge '$q$' and mass '$m$' moves in a circular orbit of radius '$r$' with angular speed '$\omega$'. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends upon