Home
Class 12
PHYSICS
A thin fixed ring of radius 'R' and posi...

A thin fixed ring of radius 'R' and positive charge 'Q' is placed in a vertical plane. A particle of mass 'm' and negative charge 'q' is placed at the centre of ring. If the particle is given a small horizontal displacement, show that it executes SHM. Also find the time period of small oscillations of this particle, about the centre of ring. (Ignore gravity)

Text Solution

AI Generated Solution

To solve the problem, we will follow these steps: ### Step 1: Understanding the Setup We have a thin fixed ring of radius \( R \) with a positive charge \( Q \) and a particle of mass \( m \) and negative charge \( q \) placed at the center of the ring. When the particle is displaced slightly from the center, we need to analyze the forces acting on it. **Hint:** Visualize the system and identify the forces acting on the particle when it is displaced. ### Step 2: Electric Field at the Center of the Ring ...
Promotional Banner

Similar Questions

Explore conceptually related problems

A positive charge Q is uniformly distributed along a circular ring of radius R .a small test charge q is placed at the centre of the ring.

A positive charge Q is uniformly distributed along a circular ring of radius R .a small test charge q is placed at the centre of the ring .The

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 smooth chute is made in a dielectric sphere of radius R and uniform volume charge density. rho . A charge particle of mass m and charge -q is placed at the centre of the sphere. Find the time period of motion of the particle?

Two charges, each equal to q, aer kept at x=-a and x=a on the x-axis. A particle of mass m and charge q_0=q/2 is placed at the origin. If charge q_0 is given a small displacement (ylt lt a) along the y-axis, the net force acting on the particle is proportional to

A thin fixed ring of radius a has a positive chage q unformly distributed over it.A particle of mass m having a megative charge Q, is placed on the axis at a distance of x(xltlta) form the center of the ring. Show that the motion of the negatively chaged particle is approximatly simple harmonic. Calculate the time period of oscillation.

Two particles A and B , each carrying charge Q are held fixed with a separation D between them. A particle C having mass m and charge q is kept at the middle point of the line AB. If particle C is displaced through a distance x along the line AB. What will be the time period of the oscillations.

A thin circular wire of radius r has a charge Q. If a point charge q is placed at the centre of the ring, then find the increase in tension in the wire.

A positive charge q is placed in a spherical cavity made in a positively charged sphere. The centres of sphere and cavity are displaced by a small distance vec(l) . Force on charge q is :

A particle of mass m and charge q is located midway between two fixed charged particles each having a charge q and a distance 2l apart. Prove that the motion of the particle will be SHM if it is displaced slightly along the line connecting them and released. Also find its time period.