An infinitely long, straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown, in the figure. The connector has length $$l$$ and resistance R. It slides to the right with a velocity v. The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is :

A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil?
Three positions shown describe :
(a) the magnet's entry
(b) magnet is completely inside and
(c) magnet's exit.

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate $${{dB} \over {dt}}$$ = 0.032 Ts^–1. The induced current in the loop is close to (Resistivity of the metal wire is 1.23 $$ \times $$ 10^–8 $$\Omega $$m)

An elliptical loop having resistance R, of semi major axis a, and semi minor axis b is placed in magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency $$\omega $$, the average power loss in the loop due to Joule heating is :