A non-conducting disc of radius a and uniform positive surface charge density sigma is placed on the ground, with its axis vertical. A particle of mass m and positive charge q is dropped, along the axis of the disc, from a height H with zero initial velocity. The particle has `q//m=4 in_0 g//sigma`
Find the value of H if the particle just reaches the disc.

A circular ring of radius R with uniform positive charge density lambda per unit length is located in the y z plane with its center at the origin O. A particle of mass m and positive charge q is projected from that point p( - sqrt(3) R, 0,0) on the negative x - axis directly toward O, with initial speed V. Find the smallest (nonzero) value of the speed such that the particle does not return to P ?

The region between x=0 and x=L is filled with uniform steady magnetic field B_0hatk . A particle of mass m, positive charge q and velocity v_0hati travels along x-axis and enters the region of the magnetic field. Neglect the gravity throughout the question. Find the value of L if the particle emerges from the region of magnetic field with its final velocilty at an angel 30^@ to its initial velocity.

An inclined plane making an angle of 30^@ with the horizontal is placed in a uniform horizontal electric of 100 V m^-1 as shown in the figure A particle of mass 1 kg and charge 0.01 C is allowed to slide down from rest from a height of 1 m. If the coefficient of frictio nis 0.2, find the time it will take the particle to reach the bottom.

A point particle of mass M is attached to one end of a massless rigid non-conducting rod of length L. Another point particle of the same mass is attached to the other end of the rod. The two particles carry charges +q and -q respectively. This arrangement is held in a region of a uniform electric field E such that the rod makes a small angle theta (say of about 5 degree) with the field direction, fig. Find an expression for the minimum time needed for the rod to become parrallel to the field after it is set free.

A wire loop carrying a current I is placed in the xy-plane as shown in figure If a particle charge +Q and mass m is placed at in centre P and given a velocity v along NP (see figure), find its instaneous acceleration.

Two uniformly large parallel thin plates having charge densities +sigma and -sigma are kept in the X-Z plane at a distance 'd' apart. Sketch an equipotential surface due to electric field between the plates. IF a particle of mass m and charge -q remains stationary between the plates, what is the magnitude and direction of this field?

A magnetic field vecB is confined to a region r le a and points out of the paper (the z axis), r = 0 being the centre 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 centre at the origin. The ring is free to rotate and is at rest. the magnetic field is brought to zero in time Deltat . Find the angular velocity omega of the ring after the field vanishes.

A particle of mass m and charge (-q) enters the region between the two charged plates initially moving along x-axis with speed v_x. The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is qEL^2//(2m v_x^2) .

A rectangular loop PQRS made from a uniform wire has length a, width b and mass m. It is free to rotate about the arm PQ, which remains hinged along a horizontal line taken as the y-axis (see figure). Take the vertically upward direction as the z-axis. A uniform magnetic field vec(B) = (3 hat(i) + 4hat(k)) B_(0) exists in the region. The loop is held in the x-y plane and a current I is passed through it. The loop is now released and is found to stay in the horizontal position in equilibrium What is the direction of the current I in PQ?

A line charge lambda per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non-conducting spokes and is free to rotate without friction about its axis (Fig. 6.22). A uniform magnetic field extends over a circular region within the rim. It is given by, B = -B_0k (r oversetlarr a, a