A rectangular loop of wire ABCD is kept close to an infinitely long wire carrying a current for 0 ≤ t ≤ T and I (0) = 0 for t > T (Fig. 6.14). Find the total charge passing through a given point in the loop, in time T. The resistance of the loop is R.

ODBAC is a fixed rectangular conductor of negligible resistance (CO is not connected) and OP is a conductor which rotates clockwise with an angular velocity (Fig 6.12). The entire system is in a uniform magnetic field B whose direction is along the normal to the surface of the rectangular conductor ABDC. The conductor OP is in electric contact with ABDC. The rotating conductor has a resistance of λ per unit length. Find the current in the rotating conductor, as it rotates by 180°.

Consider an infinitely long wire carrying a current I(t), with . Find the current produced in the rectangular loop of wire ABCD if its resistance is R (Fig. 6.13).

A magnetic field B is confined to a region r ≤ a and points out of the paper (the z-axis), r = 0 being the center of the circular region. A charged ring (charge = Q) of radius b, b >a and mass m lies in the x-y plane with its center at the origin. The ring is free to rotate and is at rest. The magnetic field is brought to zero in time Δt. Find the angular velocity of the ring after the field vanishes.

A rod of mass m and resistance R slides smoothly over two parallel perfectly conducting wires kept sloping at an angle θ with respect to the horizontal (Fig. 6.15). The circuit is closed through a perfect conductor at the top. There is a constant magnetic field B along the vertical direction. If the rod is initially at rest, find the velocity of the rod as a function of time.