A circular ring of radius R with uniform positive charge density `lambda` per unit length is located in the y-z plane with its centre at the origin O. A particle of mass m and positive charge q is projected from the point P `(Rsqrt3, 0, 0)` on the positive x-axis directly towards O, with an initial speed v. Find the smallest (non-zero) value of the speed v such that the particle does not return to P.

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 ?

A circular ring of radius R and uniform linear charge density +lamdaC//m are kept in x - y plane with its centre at the origin. The electric field at a point (0,0,R/sqrt(2)) is

A positively charged thin metal ring of radius R is fixed in the xy plane with its centre at the origin O. A negatively charged particle P is released from rest at the point (0, 0, z_0) where z_0gt0 . Then the motion of P is

A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field vecE at the centre O is

A particle of mass m and having a positive charge q is projected from origin with speed v_(0) along the positive X-axis in a magnetic field B = -B_(0)hatK , where B_(0) is a positive constant. If the particle passes through (0,y,0), then y is equal to

A Circular ring of radius 3a is uniformly charged with charge q is kept in x-y plane with center at origin. A particle of charge q and mass m is projected frim x=4 towards origin. Find the minimum speed of projection such that it reaches origin.

A circular ring lying in the x-y plane with its centre at the origin carries a uniformly distributed positive charge. The variation of the electric field E at the point (0,0,z) is correctly represented by the graph is

A particle of mass m and positive charge q is projected with a speed of v_0 in y–direction in the presence of electric and magnetic field are in x–direction. Find the instant of time at which the speed of particle becomes double the initial speed.

A nonconducting disk 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 disk, from a height H with zero initial velocity. The particle has q//m = 4 epsilon_(0) g// sigma . (i) Find the value of H if the particle just reaches the disk. (ii) Sketch the potential energy of the particle as a function of its height and find its equilibrium position.