[" Iparticle of mass "m," charge - "Q" is constrained to move along the axis of a ring of rat "],[" rries a uniform charge density "+lambda" along its a croumference.Initially,the particle li "],[" ring at a point where no net force acts on it.The period of oscillation of the "p" ."],[" laced slightly from its equilibrium position is "],[qquad (5)/(8)=(5)/(2)]

A particle of mass m and charge -Q is constrained to move along the axis of a ring of radius a. The ring carries a uniform charge density +lamda along its length. Initially, the particle is in the centre of the ring where the force on it is zero. Show that the period of oscillation of the particle when it is displaced slightly from its equilibrium position is given by T=2pisqsqrt((2epsilon_0ma^2)/(lamdaQ))

A particle of mass m and charge -Q is constrained to move along the axis of a ring of radius a. The ring carries a uniform charge density +lamda along its length. Initially, the particle is in the centre of the ring where the force on it is zero. Show that the period of oscillation of the particle when it is displaced slightly from its equilibrium position is given by T=2pisqsqrt((2epsilon_0ma^2)/(lamdaQ))

A small particle of mass m and charge-q is placed at point P on the axis of uniformly chrarged ring and releases. If R gtgt x , the particle will undergo oscillations along the axis of symmetry with an angurlar frequency that isequal to- .

Positive charge Q is distributed uniformly over a circular ring of radius R. A particle having a mass m and a negative charge q, is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming x ltltR, find the time period of oscillation of the particle if it is released from there.

Positive charge Q is distributed uniformly over a circular ring of radius R. A particle having a mass m and a negative charge q, is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming x is very less than R, find the time period of oscillation of the particle if it is released from there.

Positive charge Q is distributed uniformly over a circular ring of radius R. A particle having a mass m and a negative charge q, is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming x is very less than R, find the time period of oscillation of the particle if it is released from there.

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 (a) Find the value of H if the particle just reaches the disc. (b) Sketch the potential energy of the particle as a function of its height and find its equilibrium position.

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.

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.

A charged particle of mass m having charge q remains in equilibrium at height d above a fixed charge Q . Now the charged particle is slightly displaced along the line joining the charges, show that it will executes S.H.M. and find the time period of oscillation.