Two wires $P$ and $Q$ are made of the same material. The wire $\mathbf{Q}$ has twice the diameter and half the length as that of wire $P$. If the resistance of wire $P$ is $R$, the resistance of the wire $Q$ will be

A 1 cm segment of a wire lying along $x$-axis carries current of 0.5 A along $+x$ direction. A magnetic field $\vec{B}=(0.4 \mathrm{mT}) \hat{j}+(0.6 \mathrm{mT}) \hat{k}$ is switched on, in the region. The force acting on the segment is

A coil has 100 turns, each of area $0.05 \mathrm{~m}^2$ and total resistance $1.5 \Omega$. It is inserted at an instant in a magnetic field of 90 mT , with its axis parallel to the field. The charge induced in the coil at that instant is

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m . The number of turns in the solenoid should be