A conducting rod `PQ` of mass `m` and length `l` is placed on two long parallel (smooth and conducting) rails connected to a capacitor as shown. The rod `PQ` is connected to a non conducting spring of spring constant `k`, which is initially in relaxed state. The entire arrangement is placed in a magnetic feild perpendicular to the plane of figure.
Neglect the resistance of the rails and rod.
Now, the rod is imparted a velocity `v_(0)` towards right, then acceleration of the rod as a function of its displacement `x` given by

A conducting rod MN of mass m and length 'l' is placed on parallel smooth conducting rails connected to an uncharged capacitor of capacitance C and a battery of emf epsilon as shown. A uniform magnetic field B is existing perpendicular to the plane of the rails. The steady state velocity acquired by the conducting rod MN after closing switch S is (neglect the resistance of the parallel rails and the conducting rod)

A conducting rod MN of mass m and length 'l' is placed on parallel smooth conducting rails connected to an uncharged capacitor of capacitance C and a battery of emf epsilon as shown. A uniform magnetic field B is existing perpendicular to the plane of the rails. The steady state velocity acquired by the conducting rod MN after closing switch S is (neglect the resistance of the parallel rails and the conducting rod)

A uniform rod AB of mass m and length l is placed over two smooth conducting rails P and Q. If the witch shown as closed at t=0, find the velocity of rod AB as a function of time.

A rod PQ is connected to the capacitor plates. The rod is placed in a magnetic field (B) directed downwards perpendicular to the plane of the paper. If the rod is pulled out of magnetic field with velocity vec(v) as shown in Figure.

A rod PQ is connected to the capacitor plates. The rod is placed in a magnetic field (B) directed downwards perpendicular to the plane of the paper. If the rod is pulled out of magnetic field with velocity vec(v) as shown in Figure.

In a cylindrical region uniform magnetic field which is perpendicular to the plane of the figure is in increasing with time and a conducting rod PQ is placed in the region.If C is the centre of the circle then

In a cylindrical region uniform magnetic field which is perpendicular to the plane of the figure is in increasing with time and a conducting rod PQ is placed in the region.If C is the centre of the circle then

A straight horizontal conductor PQ of length l, and mass_ m slides down on two smooth conducting fixed parallel rails, set inclined at an angle 9 to the horizontal as shown in figure-5.30. The top end of the bar are connected with a capacitor of capacitance C. The system is placed in a uniform magnetic field, in the direction perpendicular to the inclined plane formed by the rails as shown in figure. If the resistance of the bars and the sliding conductor are negligible calculate the acceleration of sliding conductor as a function of time ifit is released from rest at t= 0

A conducting rod of length L slides at a constant velocity V on two parallel conducting rails as shown in figure. The mechanical power required to pull the rod at constant velocity is