Two parallel conducting rails separated by a distance I are fixed on a plane surface, inclined at an angle `alpha` to the horizontal as shown in figure-5.336. Rails are connected at the bottom by a resistance R. A copper rod of mass in slides without friction on the rails due to gravity. A uniform vertical field B exists throughout the region. Find the steady state velocity of the rod. Show that the rate at which thermal energy is produced in the circuit is equal to the rate at which rod is losing gravitational potential energy. What will happen if the direction of B is reversed?

Two vertical conducting rails separted by distance 1.0m are placed parallel to z -axis as shown in figure. At z=0 , a capacitor of 0.15 F is connected between the rails and a metal rod of mass 100g placed across the rails slides down along the rails. if a constant magnetic fields of 2.0 T exists perpendicular to the plane of the rails, what is the acceleration of the rod?

A conducting wire xy of lentgh l and mass m is sliding without friction on vertical conduction rails ab and cd as shown in figure. A uniform magnetic field B exists perpendicular to the plane of the rails, x moves with a constant velocity of

Consider parallel conducting rails separated by a distance l. There exists a uniform magnetic field B perpendicular to the plane of the rails as shown in Fig. Two conducting wires each of length l are placed so as to slide on parallel conducting rails. One of the wires is given a velocity v_(0) parallel to the rails. Till steady state is achieved, loss in kinetic energy of the system is

A copper rod of mass m slides under gravity on two smooth parallel rails l distance apart set at an angle theta to the horizontal. At the bottom, the rails are joined by a resistance R . There is a uniform magnetic field perpendicular to the plane of the rails. the terminal valocity of the rod is

Two parallel long smooth conducting rails separated by a distance l are connected by a movable conducting connector of mass m . Terminals of the rails are connected by the resistor R and the capacitor C as shown in figure. A uniform magnetic field B perpendicular to the plane of the rail is switched on. The connector is dragged by a constant force F . Find the speed of the connector as a function of time if the force F is applied at t = 0 . Also find the terminal velocity of the connector.

A rod of mass m , length l and resistance R is sliding down on a smooth inclined parallel rails with a cinstant velocity v . If a uniform horizontal magnetic field B exists, then find thevalue of B .

A wire ab of length l, mass m and resistance R slides on a smooth thick pair of metallic rails joined at the bottom as shown in fig. The plane of the rails makes an angle theta with the horizontal. A vertical magnetic field B exist in the region. If the wire slides on the rails at a constant speed v, then the value of B is -

Shows a rod of length l and resistance r moving on two rails shorted by a resistance R . A uniform magnetic field B is present normal to the plane of rod and rails. Show the electrical equivalence of each branch.

Two long parallel horizontal rails a, a distance d aprt and each having a risistance lambda per unit length are joing at one end by a resistance R. A perfectly conduction rod MN of mass m is free to slide along the rails without friction (see figure). There is a uniform magnetic field of induction B normal to the plane of the paper and directed into the paper. A variable force F is applied to the rod MN such that, as the rod moves a constant current flows through R. (i) Find the velocity of the rod and the applied force F as function of the distance x of the rod from R. (ii) What fraction of the work done per second by F is converted into heat?