A metallic square loop A B C D of side $15 \mathrm{cm}$ and resistance $1\Omega$ is moved at a uniform velocity of $v{ \mathrm{ms}}^{-1}$, in a uniform magnetic field of $2$ tesla, the field lines being normal to the plane of the paper Fig. The loop is connected to an electrical network of resistors, each of resistance $2\mathrm{\Omega }$. Calculate the speed of the loop.

 

A $0.5\mathrm{m}$ long metal rod PQ Fig  completes the circuit as shown. The area of the circuit is perpendicular to the magnetic field of flux of density $0.15 \mathrm{T}$. If the resistance of the total circuit is $3\Omega$, calculate the force needed to move the rod in the direction as indicated with a constant speed of $2{ \mathrm{ms}}^{-1}$

What is the self-inductance of an air core solenoid $1 \mathrm{m}$ long, diameter $0.05 \mathrm{m}$, if it has $700$ turns ?