A copper rod of mass m slides under gravity on two smooth parallel rails, with separation l and set at an angle of $$\theta $$ with the horizontal. At the bottom rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the igure. The terminal speed of the copper rod is :

A thin rod MN, free to rotate in the vertical plane aboutthe fixed end N, is held horizontal. When the end M is released the speed of this end, when the rod makes an angle $$\alpha $$ with the horizontal, will be proportional to : (see figure)

At the center of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity $$\omega $$ about an axis along their common diameter. Calculate the emf induced in their smaller coil after a time t of its start of rotation.

A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 $$ \times $$ 10^-2 m. The magnetic field at the center of the triangle will be :